Algebra & Trig (11th Edition)

Chapter 11

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

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. ; An augmented matrix is formed by the ... more

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 . ; It is observed that in the matrix , the ... more

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In an augmented matrix, the entries on the left ... more

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Yes, it is an reduced row-echelon form. ; A matrix... more

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. ; The system consists of 3 linear equations with... more

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No solutions. ; In an augmented matrix, the ... more

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. ; In an augmented matrix, the entries on the ... more

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; infinitely many solutions. ; The system consists... more

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Row-equivalent. ; The operations are done on the ... more

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Reduced row-echelon form. ; A matrix is in a row-... more

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. ; The dimension of the matrix is , where is the... more

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. ; The dimension of the matrix is , where is the... more

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. ; The dimension of the matrix is , where is the... more

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. ; The dimension of the matrix is , where is the... more

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. ; The dimension of the matrix is , where is the... more

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. ; The dimension of the matrix is , where is the... more

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. ; The dimension of the matrix is , where is the... more

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. ; The dimension of the matrix is , where is the... more

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. ; Augmented matrix is the matrix made by the ... more

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. ; Augmented matrix is the matrix made by the ... more

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. ; An augmented matrix is the matrix made by the ... more

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. ; An augmented matrix is the matrix made by the ... more

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. ; An augmented matrix is the matrix made by the ... more

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. ; An augmented matrix is the matrix made by the ... more

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. ; The augmented matrix has 2 rows and 3 columns... more

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. ; The augmented matrix has 2 rows and 3 columns... more

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. ; The augmented matrix has 3 rows and 4 columns... more

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; The augmented matrix has 3 rows and 4 columns ... more

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. ; The augmented matrix has 4 rows and 5 columns... more

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. ; The augmented matrix has 4 rows and 5 columns... more

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 . ; The given original matrix is .The new row ... more

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Add 3 times row 1 to row 2. ; The given original ... more

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Interchange row 1 and row 2.Add 4 times row 1 to ... more

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Add 2 times row 1 to row 2 Add 5 times row 1 to ... more

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2. ; The given matrix is .To obtain the new matrix... more

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2. ; On comparison of the matrix with the matrix... more

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-7. ; On comparison of the matrix with the matrix... more

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-4. ; On comparison of the matrix with the matrix... more

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14, -11. ; On comparison of the matrix with the ... more

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-7, -3. ; On comparison of the matrix with the ... more

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-2, 6. ; On comparison of the matrix with the ... more

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2, 4, . ; On comparison of the matrix ;;, it is ... more

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Yes, It is a reduced row-echelon form.  ; The ... more

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Not in row-echelon form of the matrix. ; The ... more

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Not in row-echelon form of the matrix. ; The ... more

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Row-echelon form of the matrix. ; The matrix has ... more

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. ; Use the row operation in the matrix for the ... more

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. ; Use the row operation in the matrix for the ... more

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. ; To obtain the row echelon form, use the row ... more

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. ; The matrix is .The matrix can only be in row-... more

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. ; Use the Graphing Utility/ Computer Algebra ... more

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. ; Use the Graphing Utility/ Computer Algebra ... more

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. ; Use the Graphing Utility/ Computer Algebra ... more

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. ; Use the Graphing Utility/ Computer Algebra ... more

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. ; In an augmented matrix, the entries on the ... more

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 . ; In an augmented matrix, the entries on the ... more

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. ; In an augmented matrix, the entries on the ... more

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. ; In an augmented matrix, the entries on the ... more

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. ; In an augmented matrix, the entries on the ... more

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; In an augmented matrix, the entries on the left... more

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; In an augmented matrix, the entries on the left... more

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. ; In an augmented matrix, the entries on the ... more

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. ; In an augmented matrix, the entries on the ... more

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. ; In an augmented matrix, the entries on the ... more

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No Solution. ; In an augmented matrix, the entries... more

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No solution. ; In an augmented matrix, the entries... more

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. ; In an augmented matrix, the entries on the ... more

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. ; In an augmented matrix, the entries on the ... more

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. ; The dimension of the matrix is ; so, it ... more

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. ; The dimension of the matrix is ; so, it ... more

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. ; In an augmented matrix, the entries on the ... more

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. ; In an augmented matrix, the entries on the ... more

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. ; In an augmented matrix, the entries on the ... more

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. ; In an augmented matrix, the entries on the ... more

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. ; In an augmented matrix, the entries on the ... more

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. ; In an augmented matrix, the entries on the ... more

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. ; In an augmented matrix, the entries on the ... more

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; In an augmented matrix, the entries on the left... more

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. ; The quadratic function satisfies the ... more

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. ; The quadratic function satisfies the ... more

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. ; The quadratic function satisfies the ... more

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. ; The quadratic function satisfies the ... more

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False, as in the matrix , there are two horizontal... more

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False, it is not necessary for the matrix to get ... more

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The matrix is not in the reduced row-echelon form... more

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, , , and ; For the matrix equation to hold good... more

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; If represents the element of and represents ... more

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; If represents the element of and represents ... more

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; Solve the matrix with the matrix addition ... more

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; To solve the given expression:Add to both ... more

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; Multiply both the matrices if the number of ... more

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; Multiply both the matrices if the number of ... more

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, has no solution. ; Multiply both matrices if ... more

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; The square of any matrix is the multiplication ... more

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, ; Use the subtraction matrix operation to find ... more

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; Vectors can be written as column matrices. It ... more

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; Rewrite the system of equations in the ... more

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; The matrix for the equipment lists E is The ... more

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Scalars ; Scalars in the matrices are the real ... more

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zero matrix ; If each element of the matrix is ... more

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; If two matrices are equal to each other, then ... more

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; If two matrices are equal to each other, then ... more

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,   ; If two matrices are equal to each other, ... more

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,   ; If two matrices are equal to each other, ... more

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; Let .Solve the matrix using the matrix addition... more

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; Let be the sum of the matrices to be ... more

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; Solve the matrix with matrix subtraction ... more

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; Solve the matrix with matrix addition ... more

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; Solve the matrix with matrix addition and ... more

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; Solve the matrix with matrix addition ... more

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; Solve the matrix using matrix addition ... more

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; First, use the distributive property to ... more

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; Solve the matrix using matrix subtraction ... more

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; Solve the matrix using matrix addition ... more

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; Solve the matrix using matrix addition ... more

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; Solve the matrix using matrix addition ... more

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; To solve for , the equation has to be rewritten... more

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; To solve for , the equation has to be rewritten... more

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The resultant matrix will have the dimension . ; ... more

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  ; Solve the matrix using matrix multiplication ... more

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The resultant matrix is not possible. ; Dimensions... more

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The resultant matrix is not possible. ; Dimensions... more

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  ; Solve the matrix using matrix multiplication ... more

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; Multiply the first two matrices.Let be , be... more

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; Multiply the first two matrices.Let be , be... more

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  ; As the two matrices are of the same order, ... more

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; As the two matrices and are of same order, ... more

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.Reflection across the axis. ; Convert the vector... more

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.Reflection across the axis. ; Convert the vector... more

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 Reflection across the line . ; Convert the vector... more

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, Reflection in the line  ; Convert the vector ... more

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Horizontal stretch along the -axis. ; Convert the ... more

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.Vertical stretch along the -axis. ; Convert the ... more

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; When the production level rises by , the new ... more

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; The rates are expected to increase no more than... more

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Each element of the matrix represents the profit ... more

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The costs of shipping models into warehouse 1 and ... more

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The wages of the workers for factories A and B ... more

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Here, denotes the proportion of voting population ... more

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FalseMatrix multiplication uses row-by-column ... more

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Find the left-hand side, that is, .To find , ... more

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Find the left-hand side, that is, .To find , ... more

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Calculate the left-hand side,, by multiplying the ... more

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Calculate the left-hand side, that is, .To find , ... more

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, ; ,,Here, is not equal to .Calculate and ... more

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; Calculate using the rules of matrix ... more

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; Let the two diagonal matrices be and . Now, ... more

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, ; Let and .Calculate and .Observe that .Hence... more

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Multiply the two matrices in order to determine ... more

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. ; According to the property of inverse matrices... more

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. ; To find the inverse of a matrix, use the fact ... more

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. ; For a matrix , compare and evaluate . ; . ; ... more

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. ; .Write the system in the form. ; . ; Using ... more

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Inverse. ; They are called inverse because they ... more

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Nonsingular.  ; A matrix that has a nonzero ... more

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.  ; If multiplication of and gives a result ... more

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.  ; If multiplication of and gives a result ... more

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. ; If multiplication of and results in an ... more

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. ; If multiplication of and equals to an ... more

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. ; If multiplication of and equals to an ... more

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. ; If multiplication of and equals to an ... more

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. ; If the multiplication of and equals an ... more

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. ; If the multiplication of and equals an ... more

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. ; For a matrix  such that , compare and evaluate... more

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. ; For a matrix  such that , compare and evaluate... more

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. ; For a matrix  such that , compare and evaluate... more

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. ; For a matrix  such that , compare and evaluate... more

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. ; Let . To find the inverse of the matrix, use ... more

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. ; Let . To find the inverse of the matrix, use ... more

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Not possible. ; Let . To find the inverse of the ... more

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Not possible. ; Let . To find the inverse of the ... more

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. ; Consider .  To find the inverse of the matrix... more

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. ; Consider .  To find the inverse of the matrix... more

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.  ; Take any graphing calculator and select the ... more

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. ; Take any graphing calculator and select the ... more

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. ; Take any graphing calculator and select the ... more

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Not possible. ; Take any graphing calculator and ... more

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. ; Take any graphing calculator and select the ... more

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. ; Take any graphing calculator and select the ... more

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. ; Open the graphing utility and choose the "... more

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. ; Open the graphing utility and choose the "... more

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. ; is a matrix that has the values , , , and , ... more

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. ; is a matrix that has the values , , , .The ... more

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An inverse does not exist. ; is a matrix that has... more

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. ; is a matrix that has the values , , , .The ... more

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. ; is a matrix that has the values , , , .The ... more

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. ; is a matrix that has the values , , , .The ... more

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. ; The given system of equations can be written ... more

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. ; The given system of equations can be written ... more

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. ; The given system of equations can be written ... more

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. ; The given system of equations can be written ... more

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. ; The given system of equations can be written ... more

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. ; The given system of equations can be written ... more

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. ; The given system of equations can be written ... more

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. ; The given system of equations can be written ... more

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. ; is a matrix that has the values , , , .. The ... more

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. ; .The values of , , , can be found by ... more

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The system is inconsistent and there is no ... more

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. ; is represented as .Then, on comparison, the ... more

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. ; If is represented as , on comparison, , , , ... more

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The system is inconsistent and there is no ... more

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. ; The given system of equations can be written ... more

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. ; The given system of equations can be written ... more

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. ; The given system of equations can be written ... more

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. ; The given system of equations can be written ... more

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. ; The given system of equations can be written ... more

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. ; The given system of equations can be written ... more

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. ; The given system of equations can be written ... more

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. ; The given system of equations can be written ... more

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100 bags for seedings.100 bags for general potting... more

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50 bags for seedings.300 bags for general potting.... more

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; The inverse of a matrix exists only if its ... more

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True. If matrix is the inverse of matrix , . ; ... more

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True, because the product of a matrix and its ... more

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For a matrix, , to be invertible, , and the ... more

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In , is a coefficient matrix, is a variable ... more

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; Adjoin the identity matrix to to form the ... more

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. ; A matrix is singular if the inverse does not ... more

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; A matrix is singular if the inverse does not ... more

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; ; To find minor , delete the first row and ... more

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-31 ; Use to find the determinant of a square ... more

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Determinant ; Modulus of any matrix results to be ... more

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Minor ; Minor of an element in a matrix is given ... more

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4 ; The determinant of the dimension matrix is ... more

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-10 ; The determinant of the dimension matrix is ... more

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16 ; The dimension of the matrix is . So, find ... more

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18 ; The dimension of the matrix is . So, find ... more

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-3 ; The dimension of the matrix is . So, find ... more

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-12 ; The dimension of the matrix is . So, find ... more

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0 ; The dimension of the matrix is . So, find the... more

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0 ; The dimension of the matrix is . So, find the... more

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0 ; The dimension of the matrix is . So, find the... more

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-24 ; The dimension of the matrix is . So, find ... more

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; The dimension of the matrix is . So, find the ... more

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; The dimension of the matrix is . So, find the ... more

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-1924 ; A graphing utility means a graphing ... more

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67213 ; A graphing utility means a graphing ... more

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0.08 ; A graphing utility means a graphing ... more

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-0.13 ; A graphing utility means a graphing ... more

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,,, and ; For the matrix , the minor of an element... more

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

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-9 ; For the matrix , the determinant is expanded ... more

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-5 ; For the matrix , the determinant is expanded ... more

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0 ; For the matrix , the determinant is expanded ... more

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-5 ; For the matrix , the determinant is expanded ... more

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0 ; The matrix is given by .The cofactors of the ... more

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3 ; The matrix is given by .The cofactors of the ... more

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-58 ; The matrix is given by .The cofactors of the... more

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0 ; The matrix is given by .The cofactors of the ... more

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72 ; The matrix is given by .As in the third ... more

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0 ; The matrix is given by .As in the third row, ... more

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0 ; The matrix is given by .As in the first column... more

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-108 ; The matrix is given by .As in the second ... more

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412 ; The matrix is given by .As in the second ... more

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-150 ; The matrix is given by .As in the first ... more

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-126 ; The matrix is given by .The matrix is a ... more

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223 ; The matrix is given by .The matrix is a ... more

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-336 ; The matrix is given by .The matrix is a ... more

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7441 ; The matrix is given as .The matrix is a ... more

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; The matrix can be constructed using the given ... more

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; The matrix can be constructed using the given ... more

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; Take a generalized matrix and consider its ... more

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; Take a generalized matrix and consider its ... more

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; Take a generalized matrix and consider its ... more

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; Take a generalized matrix and consider its ... more

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Find the determinant on the left-hand side and ... more

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Find the determinant of the left-hand side and ... more

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Find the determinant of the left-hand side and ... more

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Obtain the determinant on the left-hand side of ... more

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Find the determinant on the left-hand side of the ... more

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Find the determinant on the left-hand side of the ... more

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; Expand the determinant to obtain a quadratic ... more

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. ; Expand the determinant to obtain a quadratic ... more

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; Expand the determinant to obtain a quadratic ... more

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; Expand the determinant to obtain a quadratic ... more

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; Expand the determinant to obtain a quadratic ... more

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; Expand the determinant to obtain a quadratic ... more

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; Expand the determinant of the matrix using the ... more

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; Expand the determinant of the matrix using the ... more

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; Expand the determinant of the matrix using the ... more

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; Expand the determinant of the matrix using the ... more

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; Expand the determinant of the matrix using the ... more

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. ; Expand the determinant of the matrix using the... more

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TrueWhen all the elements of a row are zero, their... more

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TrueAssume a matrix with first row elements the ... more

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and ; Consider the two matrices and that are ... more

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The signs of the cofactors are not correct, the ... more

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; Let the coeffecient matrix for the system of ... more

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. ; Let the coeffecient matrix for the system of ... more

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. ; The area of a triangle with the vertices , and... more

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Three points , and are collinear (lie on the same... more

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. ; An equation of the line passing through the ... more

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The final image of the square, whose vertices are... more

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. ; The area of a parallelogram with the vertices... more

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. ; Assign a number for each alphabet, starting ... more

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. ; Assign numbers to each letter in alphabetic ... more

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To find the decoding matrix , partition the ... more

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Cramer's Rule. ; The concept of Cramer's Rule ... more

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Cryptogram. ; A cryptogram is a message written ... more

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 . ; Let the coefficient matrix for the system of ... more

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 . ; Let the coeffecient matrix for the system of ... more

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No solution. ; Convert the system of linear ... more

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. ; Let the coeffecient matrix for the system of ... more

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. ; Let the coefficient matrix for the system of ... more

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. ; Let the coeffecient matrix for the system of ... more

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. ; Let the coefficient matrix for the system of ... more

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. ; Let the coeffecient matrix for the system of ... more

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. ; Let , and . Evaluate the value of the ... more

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. ; The area of the triangle having vertices , and... more

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. ; The area of the triangle having vertices , and... more

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. ; The area of the triangle having vertices , and... more

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. ; The area of the triangle having vertices , and... more

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. ; The area of the triangle having vertices , and... more

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. ; The area of the triangle having vertices , and... more

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. ; The area of the triangle having vertices , and... more

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Collinear.  ; If the value of the determinant is ... more

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Not collinear. ; If the value of the determinant ... more

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Not collinear. ; If the value of the determinant ... more

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Collinear.  ; If the value of the determinant is ... more

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Collinear. ; If the value of the determinant is ... more

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Not collinear. ; If the value of the determinant ... more

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-3. ; If the points are said to be collinear, ... more

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3 ; If the points are said to be collinear, ... more

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. ; The determinant formula for the equation of ... more

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. ; The determinant formula for the equation of ... more

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. ; The determinant formula for the equation of ... more

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; An equation of the line passing through the ... more

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. ; The determinant formula for the equation of ... more

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. ; Write the vertices as column matrices... more

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. ; Write the vertices as column matrices. .The ... more

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. ; Write the vertices as column matrices. .The ... more

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. ; Write the vertices as column matrices as  .The... more

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. ; The area of parallelogram formed by the points... more

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. ; The area of parallelogram formed by the points... more

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. ; Form a matrix with the first row and second ... more

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. ; The given coordinates are of the form . ... more

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. ; Write the matrices of size for the given ... more

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. ; First, find the decoding matrix by using the ... more

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. ; First, find the decoding matrix by using the ... more

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. ; First, find the decoding matrix ..Now, ... more

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. ; First, find the decoding matrix ..Now, ... more

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. ; Let (decoding matrix), so that the last four ... more

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. ; Let is decoding matrix such that the last ... more

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. ; If a system of linear equations in variables... more

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. ; If a system of linear equations in variables... more

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True; because the resulting solutions will be ... more

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False. It can also mean that the system of ... more

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; The determinant form of area is . Substitute ... more

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; If a matrix has number of rows and number of ... more

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; If a matrix has number of rows and number of ... more

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; If a matrix has number of rows and number of ... more

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; If a matrix has number of rows and number of ... more

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; Write the coefficients of in the first column... more

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; In each row, write the first column values as ... more

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; In each row, write the first column values as ... more

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; Exchanging row with row , the matrix becomes... more

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; Perform in . ; Perform in . ; Perform in... more

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

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; In each row, write the first column values as ... more

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

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; Convert the equations into the matrix form.... more

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; Convert the equations into the matrix form.... more

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No solution ; Convert the equations into the ... more

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Infinitely many solutions ; Convert the equations ... more

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; Convert the equations into the matrix form.... more

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No solution ; Convert the equations into the ... more

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; Convert the equations into the matrix form.... more

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; Convert the equations into the matrix form.... more

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; Convert the equations in the matrix form.Write ... more

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; Convert the equations into the matrix form.... more

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; Convert the equations into the matrix form.... more

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; Convert the equations into the matrix form.... more

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; Write the coefficient of the equation in one ... more

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No solution ; Write the coefficient of the ... more

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; A matrix is equal to another matrix only if all... more

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; A matrix is equal to another matrix only if all... more

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; A matrix is equal to another matrix only if all... more

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; A matrix is equal to another matrix only if all... more

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; First, add the first two matrices and then add ... more

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; If represents the elements of matrix and ... more

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; If represents the elements of matrix , ... more

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; If represents elements of matrix and ... more

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; If represents elements of matrix and ... more

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; Multiplying a matrix with a constant is equal ... more

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; Using the properties of addition of matrices ... more

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; ; The order of the matrices and is . So, the ... more

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Not possible ; The order of the matrices and is... more

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; ; The orders of matrices and are and . So, ... more

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; The orders of the matrices and are and , ... more

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; The orders of the matrices and are and , ... more

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Not possible ; The orders of the matrices and ... more

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The matrix transforms the vector as a reflection ... more

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The matrix transforms the vector as a reflection ... more

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The matrix shrinks the original vector to half in ... more

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The matrix magnifies the original vector by a ... more

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; The matrix represents the production levels ... more

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It interprets that total charges per month by the ... more

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If is an matrix and is an matrix, then the ... more

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If is an matrix and is an matrix, then the ... more

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If is an matrix and is an matrix, then the ... more

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If is an matrix and is an matrix, then the ... more

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; The inverse of a matrix is given by the ... more

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Not possible ; The inverse of a matrix is given ... more

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; To find an inverse of a matrix , apply Gauss-... more

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; To find an inverse of a matrix , apply the ... more

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; An inverse of a matrix can be computed using ... more

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; An inverse of a matrix can be computed using ... more

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; To find the inverse of matrices, use the ... more

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; To find the inverse of a matrix, use the ... more

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No possible inverse matrix. ; For a matrix with ... more

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No possible inverse exists. ; For a matrix with ... more

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and ; Consider matrix as invertible matrix. Then... more

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, ; Consider matrix as invertible matrix. Then, ... more

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and ; Consider matrix as invertible matrix. Then... more

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and ; Consider matrix as an invertible matrix. ... more

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and ; Consider matrix as invertible matrix. Then... more

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and ; Consider matrix is invertible matrix. Then... more

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; Consider matrix is invertible matrix. Then, ... more

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, and ; Consider matrix is invertible matrix. ... more

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, and ; Consider matrix is invertible matrix. ... more

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26 ; The determinant of a matrix is given by . ... more

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1 ; The determinant of a matrix is given by . ... more

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116 ; The determinant of a matrix is given by . ... more

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-110 ; The determinant of a matrix is given by... more

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-6 ; The expression of the determinant when ... more

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-4 ; The expression of the determinant when ... more

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15 ; The expression of the determinant, when ... more

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130 ; The expression of the determinant, when ... more

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-23 ; The expression of the determinant, when ... more

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, ; The system of equations can be solved by ... more

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, ; The system of equations can be solved by ... more

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, ,   ; The system of equations can be solved by ... more

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, , ; The system of equations can be solved by ... more

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16 ; The area of a triangle with vertices , and ... more

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24 ; The area of a triangle with vertices , and ... more

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Collinear ; The determinant of three points , and... more

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Collinear ; The determinant of three points , and... more

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; The equation of a line passing through the ... more

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; The equation of a line passing through the ... more

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; The equation of a line passing through the ... more

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; The equation of a line passing through the ... more

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; The area of a parallelogram is , where equals... more

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; The area of a parallelogram is , where equals... more

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SEE YOU FRIDAY ; To decode the cryptogram, the ... more

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MAY THE FORCE BE WITH YOU ; To decode the ... more

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False; the matrix must be square. ; Determinants ... more

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TrueAny row or column of a determinant can be ... more

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Determinant of the square matrix along the row: ... more

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All are not correct at the same time. If the third... more

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. ; Use the row elimination method to convert ... more

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. ; Use the row elimination method to convert   ... more

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; The augmented matrix is a matrix in which the ... more

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;Reflection along the line . ; can be written as ... more

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; Let the given matrix be . Then, the inverse is... more

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; Let matrix = .For the existence of , . ... more

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; The inverse of the matrix is . Simplify the ... more

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-112 ; It is observed that the matrix has the ... more

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0 ; It is observed that the matrix has the same ... more

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43 ; It is observed that the matrix has the same ... more

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, ; It is observed that the set of equations can ... more

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; Find the determinant of the coefficient matrix... more

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7 ; The area of the triangle can be calculated ... more

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; Find the uncoded matrices for the given ... more

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of solution of solution ; Let be the volume in... more

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; An example of a singular idempotent matrix is... more

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;;, Thus, is verified.  ; Interchange the rows of... more

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; The inverse of a matrix is given by the ... more

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; A matrix is singular if the inverse does not ... more

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Simplify the determinant along the first row ... more

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Simplify the determinant along the first row ... more

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Simplify the determinant along the first row ... more

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; The determinant of a matrix is . Take from ... more

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; Consider the matrix and a column matrix and ... more

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;; ; Let the mass of sulfur, nitrogen, and ... more

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;; ; Let the cost of the transformer, cost of wire... more

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; Adjoin the identity matrix to form the matrix... more

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;;The determinant of the inverse of a matrix is ... more

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