Algebra and Trigonometry (6th Edition)

Chapter 10

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; The coefficients of each variable are placed to... more

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; Write the augmented matrix for the system. ; ... more

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; Write the augmented matrix for the system. ; To... more

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; Write the augmented matrix for the system. ; ... more

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matrixelements ; A rectangular array of numbers ... more

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3 ; To obtain 0 where there is -3, multiply the ... more

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; The coefficients of each variable are placed to... more

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; The matrix obtained in using Gauss-Jordan ... more

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After simplifying the matrix to row-echelon form, ... more

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Gauss-Jordan elimination does not use back ... more

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; The coefficients of each variable are placed to... more

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; The coefficients of each variable are placed to... more

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; The coefficients of each variable are placed to... more

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; The coefficients of each variable are placed to... more

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; Align the same variable in each column. The ... more

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; Align the same variable in each column. The ... more

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; Align the same variable in each column. The ... more

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; Align the same variable in each column. The ... more

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; Assign the same variable in each column. Each ... more

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; Assign the same variable in each column. Each ... more

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; Assign the same variable in each column. Each ... more

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; Assign the same variable in each column. Each ... more

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; Multiply each element of row 1 by . ; Simplify... more

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; Multiply each element of row 1 by .  ; Simplify... more

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; Multiply each element in row 1 by -3. ; Add ... more

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; Multiply each element in row 1 by -3. ; Add ... more

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; To perform , multiply each element in row 1 by... more

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; To perform , multiply each element in row 1 by... more

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; To get 0’s below the 1 in column 1, replace ... more

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; To get 0's below the 1 in column 1, replace ... more

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; Write the augmented matrix for the system. ; To... more

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; Write the augmented matrix for the system. ; ... more

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; Write the augmented matrix for the system. ; ... more

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; Write the augmented matrix for the system. ; ... more

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; Write the augmented matrix for the system. ; ... more

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; Write the augmented matrix for the system. ; ... more

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; Write the augmented matrix for the system. ; To... more

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; Write the augmented matrix for the system. ; ... more

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; Arrange the variables in the same order in each... more

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; Arrange the variables in the same order in each... more

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; Write the augmented matrix for the system. ; ... more

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; Write the augmented matrix for the system. ; ... more

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; Write the augmented matrix for the system. ; ... more

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; Write the augmented matrix for the system. ; ... more

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; Write the augmented matrix for the system. ; ... more

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; Write the augmented matrix for the system. ; ... more

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; Write the augmented matrix for the system. To ... more

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; Write the augmented matrix for the system. To ... more

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; Substitute the values of and into the given ... more

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; Substitute the values of and into the given ... more

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; Substitute the values of and into the given ... more

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; Substitute the values of and into the given ... more

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; Express the variables , , , and as natural ... more

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; Express the variables , , , and as natural ... more

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Type A: 4 oz; Type B: oz; Type C: 1 oz ; Let = ... more

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Desk C: 15; Desk O: 10; Desk D: 20 ; Let = the ... more

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122, 28, 24, and 9 ; Let , , , and be defined as ... more

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132, 35, 28, and 3 ; Let , , , and be defined as ... more

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A rectangular display of elements (usually numbers... more

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An augmented matrix is a matrix obtained from the ... more

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means elements of row are interchanged with ... more

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To solve the system of linear equations, its ... more

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Gaussian elimination uses back substitution to ... more

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13.    15.    17.   ; Using a graphing utility, ... more

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21. 23.25.27.29. ; Using a graphing utility, press... more

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; Using a graphing utility, press the MATRIX key ... more

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The statement makes sense. ; In addition method, a... more

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The statement makes sense. ; In order to solve the... more

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The statement makes sense.  ; In order to simplify... more

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The statement makes sense.  ; If the row ... more

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False; A matrix row operation which involves ... more

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False;  ; There are three variables in the system ... more

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False; use row operations to obtain a row-... more

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False; row  ; The elements in row are added to ... more

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60 units; $7700 ; Write the system of equations of... more

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; Express the first equation in terms of . ; ... more

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Replace the inequality symbol with an equal sign ... more

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; Make the coefficients 1 by using power rule... more

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; Write the equation in terms of the sine ... more

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; It satisfies the system of linear equations. ; ... more

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satisfies the system. ; Find the value of and by... more

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. ; Write the augmented matrix of the system of ... more

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; Write the augmented matrix of the system of ... more

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; Write the augmented matrix of the system.  ; To... more

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One solution. ; The augmented matrix is in row-... more

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Infinitely many solutions. ; We get if the last ... more

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If you substitute into the ordered triple, the ... more

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; ; ; ; Write the equation that corresponds to the... more

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; Write the augmented matrix of the systems of ... more

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; Write the augmented matrix of the system of ... more

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; Write the augmented matrix of the system of ... more

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; Write the augmented matrix of the system. ; To ... more

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; Write the augmented matrix of the system of ... more

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; Write the augmented matrix of the system. ; To ... more

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; Write the augmented matrix of the system. ; To ... more

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; Write the augmented matrix of the system. ; To ... more

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; Write the augmented matrix of the system. ; To ... more

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; Write the augmented matrix of the system. ; To ... more

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; Write the augmented matrix of the system. ; To ... more

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; Write the augmented matrix of the system. ; To ... more

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; Write the augmented matrix of the system. ; To ... more

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; Write the augmented matrix of the system. To ... more

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; Write the augmented matrix of the system. ; To ... more

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; Write the augmented matrix of the system. ; To ... more

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; Write the augmented matrix of the system. ; The... more

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; Write the augmented matrix of the system. ; To ... more

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; Write the augmented matrix of the system. ; To ... more

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; Write the augmented matrix of the system. ; To ... more

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; Write the augmented matrix of the system. ; To ... more

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; Write the augmented matrix of the system. ; To ... more

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; Write the augmented matrix of the system. ; To ... more

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; Write the augmented matrix of the system. ; To ... more

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; automobiles and 12 automobiles arrive ... more

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; automobiles and 6 automobiles arrive ... more

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; Write the obtained equations into its standard ... more

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; , ; Substitute into the ordered triple . ; more

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; Let be Type , be Type and be Type . Write ... more

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It is impossible to convert the augmented matrix ... more

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The row with 0’s to the left and right of the ... more

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The second method is better.  Expressing it in as ... more

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No ; The translated equation of the last row is , ... more

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Yes ; The translated equation of the last row is... more

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No ; The number of variables cannot equal the ... more

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Makes sense ; The number arriving is equal to the ... more

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; Write the augmented matrix of the system. ; To ... more

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8; ; Let be the number.  Write an equation that ... more

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; Replace with . ; Interchange and . ; Solve ... more

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4 for ; 6 for ; Let be the amount for .Let be ... more

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; Subtract from both sides of the equation. ; ... more

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; Perform the given operations. Multiply then add... more

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8 ; Simplify operations inside the bracket. ; ... more

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; Solve for by subtracting from both sides of ... more

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; The row 1, column 1, element of matrix is the ... more

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; ; The order of matrix is and matrix is . The ... more

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; A matrix is added to the original matrix to ... more

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Third ; The element is found in  row and  column... more

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; The order of the matrix has rows and columns... more

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square ; A square matrix has the same number of ... more

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-10; 6 ; If matrix = matrix , the corresponding ... more

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Commutative property of addition is true for ... more

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Matrices can be added or subtracted if they have ... more

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In scalar multiplication, a matrix is multiplied ... more

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; ; columns; rows ; The order of matrix is given ... more

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It is possible for matrices of different orders to... more

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Commutative property of multiplication is when . ... more

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; ; The given matrices are equal. Therefore, the ... more

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; ; The given matrices are equal. Therefore, the ... more

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; ; The given matrices are equal. Therefore, the ... more

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; ; The given matrices are equal. Therefore, the ... more

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; Solve for by adding to both sides of the ... more

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; Solve for by adding to both sides of the ... more

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; Solve for by subtracting to both sides of the... more

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; Solve for by subtracting to both sides of the... more

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; Solve for by subtracting to both sides of the... more

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; Solve for by subtracting to both sides of the... more

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; Solve for by subtracting to both sides of the... more

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; Solve for by subtracting to both sides of the... more

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; Isolate by multiplying both sides by  . ; ... more

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; Isolate by multiplying both sides by  . ; ... more

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; The operation is defined because both matrix ... more

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; The operation is defined because both matrix ... more

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; The order of matrix is and matrix is . The ... more

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; The sum of matrices and is defined because ... more

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The operation is undefined because both matrices ... more

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The operation is undefined because both matrices ... more

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; The order of matrix is and the product matrix... more

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; The order of matrix is and the product matrix... more

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; Make an equation that models the situation. ; ... more

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; Make an equation that models the situation. ; ... more

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Choose matrices , and to model the distributive ... more

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Choose matrices , and to model the associative ... more

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; The sign of the -coordinate is changed. ; The ... more

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; The sign of the -coordinate is changed. ; The ... more

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; A matrix is added to the original matrix to ... more

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; A matrix is added to the original matrix to ... more

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; To reduce the figure to half its perimeter, ... more

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; To reduce the figure to half its perimeter, ... more

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The order of the matrix is the dimension of the ... more

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is the element found in the th row and th column ... more

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Equal matrices are matrices with the same order ... more

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If the matrices have the same order, they can be ... more

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If the matrices have the same order, it can be ... more

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Matrices cannot be added or subtracted if they ... more

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Scalar multiplication is when a matrix is ... more

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To be able to multiply matrices,  the number of ... more

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If the number of columns in matrix is not the ... more

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The order of the product matrix is determined by ... more

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Enlarging an image can be accomplished by scalar ... more

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.  38.  39.  40.  41. undefined 42. undefined 43... more

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Does make sense. ; Matrices can be added if they ... more

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Does not make sense. ; Matrix multiplication is ... more

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Does make sense. ; Matrices can be added if they ... more

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Does make sense. ; Matrices can be multiplied if ... more

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; Assign any values for the elements of matrix . ... more

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When a square matrix with non-zero elements on the... more

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Yes. ; Substitute the matrices to the given ... more

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One interesting application of matrices is its use... more

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; Write each side of the equation as a power of ... more

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-9.64 ; Take the natural logarithm on both sides ... more

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[-8,5] ; Rewrite the inequality. ; Subtract 3 to ... more

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; Solve for using the fact that the sum of the ... more

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The elements of the product matrix are the same as... more

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; Write the augmented matrix for the system. To ... more

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; Find the product matrix of the first matrix and... more

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; Write the augmented matrix for the system.  ; ... more

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; Write the augmented matrix of the system of ... more

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; Write the augmented matrix of the equations. ; ... more

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; Write the augmented matrix of the system. ; To ... more

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; Write the augmented matrix of the system. ; ... more

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; Substitute the matrices into the equation. ; ... more

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; Substitute the matrices into the equation. ; ... more

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; Substitute the matrices into the equation. ; ... more

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The operation is undefined because both matrices ... more

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; Add to both sides of the equation. ; Isolate ... more

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is the multiplicative inverse of .  ; Solve for ... more

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; Since is a matrix, then its multiplicative ... more

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; Assign the elements with corresponding ... more

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; Since is a matrix, start by forming the ... more

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; Write the linear system in matrix form . ; The ... more

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, 10, , 77 ; Use numbers to express the word “BASE... more

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2, 1, 19, 5 or “BASE” ; Given the coding matrix , ... more

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; The identity matrix contains 1 on its main ... more

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; The identity matrix contains 1 on its main ... more

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multiplicative inverse ; Given square matrices ... more

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Suppose is a matrix with multiplicative inverse... more

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; Suppose is invertible. In this case, the ... more

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singular ; Let be a square matrix of order . If ... more

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Assign the elements of variable placers, namely... more

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; Since is invertible of order , then its ... more

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; Given that the matrix equation has a unique ... more

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  is the multiplicative inverse of . ; Solve for ... more

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  is not the multiplicative inverse of . ; Solve ... more

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  is not the multiplicative inverse of . ; Solve ... more

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  is not the multiplicative inverse of . ; Solve ... more

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   ; Find using the row-by-column definition of ... more

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   ; Find using the row-by-column definition of ... more

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   ; Find using the row-by-column definition of ... more

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   ; Find using the row-by-column definition of ... more

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   ; Find using the row-by-column definition of ... more

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   ; Find using the row-by-column definition of ... more

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   ; Find using the row-by-column definition of ... more

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   ; Find using the row-by-column definition of ... more

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; For the given matrix, , , , and . Compute .  ; ... more

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; For the given matrix, , , , and .Compute .  ; ... more

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; For the given matrix, , , , and .Compute .  ; ... more

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; For the given matrix, , , , and .Compute .  ; ... more

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does not have a multiplicative inverse.   ; For ... more

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does not have a multiplicative inverse.   ; For ... more

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; Form the augmented matrix  ; Perform the ... more

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; Form the augmented matrix  ; Perform the ... more

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; Form the augmented matrix  ; Perform the ... more

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; Form the augmented matrix  ; Replace row 3 by ... more

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; Form the augmented matrix  ; Interchange row 1 ... more

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; Form the augmented matrix  ; Interchange row 1 ... more

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; Form the augmented matrix  ; Perform the ... more

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; Form the augmented matrix  ; Interchange row 1 ... more

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; Form the augmented matrix  ; Replace row 4 by ... more

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; Form the augmented matrix  ; Replace row 1 by ... more

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; Write each equation in the form , as needed.  ... more

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; Write each equation in the form , as needed. If... more

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; Write each equation in the form , as needed.  ... more

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; Write each equation in the form , as needed.  ... more

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; Use the row-by-column definition of matrix ... more

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; Use the row-by-column definition of matrix ... more

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; Use the row-by-column definition of matrix ... more

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; Use the row-by-column definition of matrix ... more

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; Calculate , where , , , and . Note that . ; The... more

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; Calculate , where , , , and .Note that . ; The ... more

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; Find by taking the difference between the ... more

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; Find by taking the difference between the ... more

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    Observation: ; Find .  ; To find , recall that... more

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   Observation: ; Find .  ; To find , recall that ... more

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Show that and ; , , and ; Show that . ; Show that... more

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Let the multiplicative inverse . Then . Expand the... more

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Encoded message: Decoded message: or HELP ; ... more

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Encoded message: Decoded message: or LOVE ; ... more

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Encoded message: Decoded message: or SEND-CASH ; ... more

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Encoded message: Decoded message: or STAY-WELL ; ... more

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A square matrix with 1s on the main diagonal from ... more

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If and where is the identity matrix of , then ... more

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For to be possible:must have the same number of ... more

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Let , then the inverse matrix is: ; This procedure... more

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Form an augmented matrix where is the original ... more

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First, write each equation so the left hand side ... more

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To solve , multiply both sides by on the left of ... more

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A cryptogram is a numerically encoded message that... more

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The letters would first be substituted for using a... more

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The inverse of the coding matrix will be ... more

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; Using a graphing calculator or other tool, ... more

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; Using a graphing calculator or other tool, ... more

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; Using a graphing calculator or other tool, ... more

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; Using a graphing calculator or other tool, ... more

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; Using a graphing calculator or other tool, ... more

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; Using a graphing calculator or other tool, ... more

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; Convert the system of equations into a matrix ... more

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; Convert the system of equations into a matrix ... more

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; Convert the system of equations into a matrix ... more

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; Convert the system of equations into a matrix ... more

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; Convert the system of equations into a matrix ... more

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; Convert the system of equations into a matrix ... more

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Choose a coding matrix and find its inverse.Use a ... more

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Choose a coding matrix and find its inverse.Use a ... more

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Only square matrices are able to have inverse ... more

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Guass-Jordan Elimination is a possible method for ... more

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This is a common method for solving systems of ... more

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There is no one single correct coding matrix, the ... more

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False, should say some or many instead of all. ; ... more

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True ; Let and . If , then will also not equal ... more

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False, should say multiply the inverse of and... more

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False, should say ; Since , , and are invertible... more

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False, should say ; Let and . Then and  Then ... more

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False, should say is not invertible. ; For a ... more

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; All identity matrices are their own inverses... more

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; Note: the inverse of an inverse is the original... more

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; Compute for the matrix of the form:  ; Solve ... more

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Write a message and convert the message to numbers... more

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; Compress the left-hand side using the product ... more

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; Compress the left-hand side using the quotient ... more

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; Multiply the top equation by so that the sum ... more

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; The triangle involved has two sides known and ... more

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2 ; Simplify the multiplication. ; Simplify the ... more

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6 ; Simplify the multiplication. ; Simplify the ... more

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; Simplify the parentheses. ; Simplify the ... more

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; Compare the system to the given system to ... more

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80 ; Let be the given matrix. Consider the matrix... more

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; Let be the given matrix. Consider the matrix ... more

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; Compare the system and the given system to ... more

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; Choose the column or row with that contains ... more

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; The determinant of the matrix is . Here, , , ... more

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; Given a linear system with two variables  , the... more

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; The determinant of a 3x3 matrix can be solved ... more

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; Given a linear system with two variables  , the... more

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3rd column ; Expanding the given 3x3 matrix into ... more

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1 ; The determinant of the matrix is represented ... more

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; The determinant of the matrix is represented ... more

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; The determinant of the matrix is represented ... more

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; The determinant of the matrix is represented ... more

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0 ; The determinant of the matrix is represented ... more

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; The determinant of the matrix is represented ... more

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; The determinant of the matrix is represented ... more

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; The determinant of the matrix is represented ... more

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; The determinant of the matrix is represented ... more

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; The determinant of the matrix is represented ... more

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; Compare the system to the given system to ... more

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; Compare the system to the given system to ... more

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; Compare the system to the given system to ... more

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; Compare the system to the given system to ... more

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; Compare the system to the given system to ... more

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; Compare the system to the given system to ... more

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; Compare the system to the given system to ... more

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; Compare the system to the given system to ... more

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; Compare the system to the given system to ... more

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; Isolate the constants of the two linear ... more

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; Isolate the constants of the two linear ... more

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; Isolate the constants of the two linear ... more

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; Let be the given matrix. Consider the matrix ... more

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; Let be the given matrix. Consider the matrix ... more

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; Let be the given matrix. Consider the matrix ... more

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; Let be the given matrix. Consider the matrix ... more

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; Let be the given matrix. Consider the matrix ... more

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; Let be the given matrix. Consider the matrix ... more

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; Compare the system and the given system to ... more

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; Compare the system and the given system to ... more

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; Compare the system and the given system to ... more

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; Compare the system and the given system to ... more

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; Compare the system and the given system to ... more

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; Compare the system and the given system to ... more

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; Compare the system and the given system to ... more

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; Compare the system and the given system to ... more

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; Let be the given matrix. Choose the column or ... more

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; Let be the given matrix. Choose the column or ... more

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195 ; Let be the given matrix. Choose the second ... more

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48 ; Let be the given matrix. Expand the ... more

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-42 ; Begin by finding the determinants within ... more

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-407 ; Begin by finding the determinants within ... more

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; In Cramer's rule, the determinant corresponds ... more

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; In Cramer's rule, the determinant corresponds ... more

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-11 ; Let be the determinant given. Evaluate .... more

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26 ; Let be the determinant given. Evaluate .Note... more

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4 ; Let be the determinant given. Evaluate by ... more

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3 ; Let be the determinant given. Evaluate by ... more

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; Let , , and . Replace , , , , , and of the ... more

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; Let , , and . Replace , , , , , and of the ... more

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Yes, the points are collinear. ; Substitute and ... more

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Yes, the points are collinear. ; Let , , and  and ... more

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; Let  and . Replace , , , and   in the following... more

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; Let , . Replace , , , and  in the following ... more

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A second order determinant refers to a matrix ... more

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Suppose that a system of equations is given. The ... more

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A third-order determinant can be obtained by ... more

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Let be the element selected for the minor . The ... more

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Solving systems with three variables using Cramer'... more

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When using Cramer's rule, if it means the system ... more

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For an example, consider the system:  Solve for ... more

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Cramer's rule is arguably the most direct and ... more

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; Using a graphing calculator, input the matrices... more

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-2100 ; Edit the blank fields of the matrix. Enter... more

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13,200 ; Edit the blank fields of the matrix. ... more

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Represent the coefficients of the linear system as... more

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Does not make sense. A determinant can only be ... more

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Does not make sense. There is no way to speed up ... more

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Does not make sense. There is one determinant for ... more

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Does not make sense. When is 0, the system is ... more

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48 ; Apply the cofactor formula , where is the ... more

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If the original value of the determinant is ... more

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Obtain and evaluate first , and of the given ... more

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To show that the given determinant will give the ... more

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; Let be the length and be the width. Obtain ... more

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; First, apply the rational roots theorem.List ... more

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Expanding right-hand expression gives Using the ... more

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; Divide both sides by 400. ; Simplify. ; more

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; Group the terms with and variables separately... more

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; Multiply each element in row 2 by -5. ; Add ... more

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; Multiply each element in row 1 by . ; Simplify... more

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; Write the augmented matrix for the system.  ; ... more

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; Write the augmented matrix for the system.  ; ... more

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; Write the augmented matrix for the system.  To ... more

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1% capitalist; 15% upper middle; 34% lower middle... more

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; Write the augmented matrix of the system of ... more

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; Write the augmented matrix of the equations. ; ... more

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; Write the augmented matrix of the equations. ; ... more

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; Write the augmented matrix of the equations. ; ... more

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; ; ; The given matrices are equal. Therefore, the... more

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; The matrices have the same order, which is . ... more

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; Multiply each element in matrix by 2. ; ... more

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; The matrices have the same order, which is .... more

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The operation is undefined because both matrices ... more

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; The operation is defined because both matrix ... more

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; The operation is defined because both matrix ... more

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; The operation is defined because both matrix ... more

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; The order of matrix is and matrix is . The ... more

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; The order of matrix is and matrix is . The ... more

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; The order of matrix is and matrix is . The ... more

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; The order of matrix is and matrix is . The ... more

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The operation is not possible because the product ... more

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; The order of matrix is and matrix is . The ... more

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; The order of matrix is and matrix is . The ... more

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; Solve for by subtracting from both sides of ... more

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; Find the numbers that represent the specific ... more

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; A matrix is added to the original matrix to ... more

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; A matrix is added to the original matrix to ... more

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; To reduce the figure to half its perimeter, ... more

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; Find the product matrix . For row 1 of , find ... more

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; Find the product matrix . For row 1 of , find ... more

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; Find the product matrix . For row 1 of , find ... more

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; Find the product matrix . For row 1 of , find ... more

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; Find the product of matrix and . For row 1 of ... more

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; Find the product of matrix and . For row 1 of ... more

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; Assign elements as , , , and . Substitute the ... more

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; Assign elements as , , , and .Substitute the ... more

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; Write the augmented matrix . ; Use Gauss-Jordan... more

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; Write the augmented matrix . ; Use Gauss-Jordan... more

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,    ; Write the corresponding numbers for the ... more

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; Move from left to right.  Multiply the number ... more

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; Move from left to right.  Multiply the number ... more

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; Choose a row or column to use to find the ... more

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; Choose a row or column to use to find the ... more

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; Choose a row or column to use to find the ... more

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; Choose a row or column to use to find the ... more

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; According to Cramer’s Rule, the solution to a ... more

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; According to Cramer’s Rule, the solution to a ... more

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; According to Cramer’s Rule, the solution to a ... more

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; According to Cramer’s Rule, the solution to a ... more

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, The average number for those aged is , The ... more

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; Check the system to confirm that the equations ... more

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, where is any real number ; Check the system to ... more

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; Find by multiplying each element of matrix by... more

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; Matrix is and matrix is .  To multiply ... more

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; If , then  .  Substitute , , and into the ... more

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; Matrix is and matrix is .  To multiply ... more

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Construct . Write as and as .  Multiply by .  ... more

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18 ; Choose a row or column to use to find the ... more

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; According to Cramer’s Rule, .  First, construct... more

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; Write the equation in standard form with on ... more

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; Distribute to remove parentheses.  Then, ... more

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; Clear one of the radicals by isolating the ... more

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; Consider the zeros of the function .Since the ... more

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; Substitute to rewrite the equation.  Note that... more

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; Use the logarithmic property to combine the ... more

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, ; Replace with .  Because the principal square ... more

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First, factor the denominator.  The denominator of... more

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; Consider the -intercepts of the function.is an... more

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Write the logarithm in exponential form:  If , ... more

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; Matrix is and matrix is .  To multiply ... more

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Substitute values of into the equation and find ... more

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The equation is written in the form , which is a ... more

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