Algebra and Trigonometry (4th Edition)

Chapter 13

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Dependent ; The system is called dependent if the ... more

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

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; The dimension of a matrix is given by where ... more

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; The dimension of a matrix is given by where ... more

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; The dimension of a matrix is given by where ... more

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; The dimension of a matrix is given by where ... more

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; The dimension of a matrix is given by where ... more

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; The dimension of a matrix is given by where ... more

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

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

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; Do not change the first or third row in the ... more

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; Do not change the first or third row in the ... more

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; Do not change the first or second row in the ... more

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; Do not change the first or second row in the ... more

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; Write the equivalent augmented matrix. ; ... more

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; Write the equivalent augmented matrix.  ; ... more

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; Write the equivalent augmented matrix.  ; ... more

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; Write the equivalent augmented matrix.  ; ... more

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; Write the equivalent augmented matrix.  ; ... more

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; Write the equivalent augmented matrix. ; ... more

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; Write the equivalent augmented matrix. ; ... more

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; Write the equivalent augmented matrix. ; ... more

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; Write the equivalent augmented matrix. ; ... more

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; Write the equivalent augmented matrix.  ; ... more

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No solution ; Write the equivalent augmented ... more

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No solution ; Write the equivalent augmented ... more

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Dependent; , where is any real number ; Write the... more

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Dependent; , where is any real number ; Write the... more

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No solution ; Write the equivalent augmented ... more

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Dependent; , where is any real number ; Write the... more

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Dependent; , where is any real number ; Write the... more

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Dependent; , where is any real number ; Write the... more

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Dependent; ; Write the equivalent augmented matrix... more

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No solution ; Write the equivalent augmented ... more

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; Write the equivalent augmented matrix. ; ... more

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; Write the equivalent augmented matrix.  ; ... more

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No solution ; Write the equivalent augmented ... more

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Dependent; , where is any real number ; Write the... more

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; Write the equivalent augmented matrix.  ; ... more

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no solution ; Determine the corresponding ... more

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, where is a real number ; Determine the ... more

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; Determine the corresponding augmented matrix of... more

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; Determine the corresponding augmented matrix of... more

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; Determine the corresponding augmented matrix of... more

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; Determine the corresponding augmented matrix of... more

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; Determine the corresponding augmented matrix of... more

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, where and are real numbers ; Determine the ... more

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, where is a real number ; Determine the ... more

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, where is a real number ; Determine the ... more

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, where is a real number ; Determine the ... more

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, , ; Determine the corresponding augmented matrix... more

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, , ; Determine the corresponding augmented matrix... more

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, , , ; Determine the corresponding augmented ... more

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, , , ; Determine the corresponding augmented ... more

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2 , 1 , 2 ; Let , , and be the number of , , and... more

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40 mL of solution, 50 mL of solution, 10 mL of ... more

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: 5 miles: 2 miles: 30 miles ; Let , , and be the... more

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: 20 students: 50 students: 30 students ; Let , , ... more

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impossible ; Let , , and be the 3 furnitures.Set ... more

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, , , and , where ; Let , , , and be the given ... more

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, , , ; Let and . Substitute these values into an... more

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dimension ; Let the dimensions of matrices and ... more

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The sum of two matrices and is defined only if ... more

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; Let and be the first and second matrices in ... more

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not equal ; One of the requirements for two ... more

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equal ; Two matrices are said to be equal if:they ... more

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, ; The given matrices and are equal if their ... more

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, ; The given matrices and are equal if their ... more

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; Since the matrices to be added have the same ... more

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; Since the matrices to be subtracted have the ... more

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; Find the scalar product by multiplying each ... more

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The sum is undefined because the dimensions of the... more

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The product of the given matrices is undefined due... more

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; Let and be the fist and second matrices in ... more

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; Let and be the fist and second matrices in ... more

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; Let and be the fist and second matrices in ... more

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; Isolate on one side of the equation.Subtract ... more

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The equation has no solution because the sum of ... more

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The equation has no solution because the sum of ... more

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; Isolate on one side of the equation.Multiply ... more

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; Isolate on one side of the equation.Multiply ... more

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; Isolate on one side of the equation.Subtract ... more

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  ; Since the number of columns of the matrix is ... more

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The product is undefined since the number of ... more

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; Since the number of columns of the matrix is ... more

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; Since the number of columns of the matrix is ... more

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The sum is undefined since the dimensions of is ... more

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; Since matrix is a square matrix, the number of... more

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; Equate the elements of first row of the matrix ... more

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; Multiply the scalar on the matrix at the left ... more

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; Multiply the scalar on the matrix at the left ... more

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; Perform the subtraction operation on the left ... more

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; Write the system of equation in the form of a ... more

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; Write the system of equation in the form of a ... more

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; Write the system of equation in the form of a ... more

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; Write the system of equation in the form of a ... more

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Only is defined.  ; For the given operation , the... more

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The matrices and must have dimensions in the ... more

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; Write the entries of the product as the inner... more

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; Write the entries of the product as the inner... more

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, , , , , , ; Write the entries of the product ... more

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To verify that is the inverse of , show that and... more

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To verify that is the inverse of , show that and... more

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To verify that is the inverse of , show that and... more

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To verify that is the inverse of , show that and... more

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; is the inverse of . ; Find the inverse of ... more

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; is the inverse of . ; Find the inverse of by ... more

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; is the inverse of . ; Set the graphing utility ... more

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; is the inverse of . ; Set the graphing utility ... more

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; Let be the given matrix. Find the inverse of ... more

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; Let be the given matrix. Find the inverse of ... more

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; Let be the given matrix. Find the inverse of ... more

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; Let be the given matrix. Find the inverse of ... more

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No inverse ; Let be the given matrix. Find the ... more

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; Let be the given matrix. Find the inverse of ... more

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; Let be the given matrix. Find the inverse of ... more

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; Let be the given matrix. Form a matrix \(\left... more

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; Let be the given matrix. Form a matrix \(\left... more

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; Let be the given matrix. Form a matrix \(\left... more

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No inverse ; Let be the given matrix. Form a ... more

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; Let be the given matrix. Form a matrix \(\left... more

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; Let be the given matrix. Form a matrix \(\left... more

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; Let be the given matrix. Form a matrix \(\left... more

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; Let be the given matrix. Form a matrix \(\left... more

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No inverse ; Let be the given matrix. Form a ... more

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; Set the graphing utility to Matrix mode. Some ... more

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; Set the graphing utility to Matrix mode. Some ... more

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; Set the graphing utility to Matrix mode. Some ... more

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; Set the graphing utility to Matrix mode. Some ... more

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; Set the graphing utility to Matrix mode. Some ... more

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; Set the graphing utility to Matrix mode. Some ... more

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; Set the graphing utility to Matrix mode. Some ... more

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; Set the graphing utility to Matrix mode. Some ... more

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; Set the graphing utility to Matrix mode. Some ... more

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; Find using the matrices and used in question... more

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; Find using the matrices and used in question... more

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; Find using the matrices and used in question... more

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, ; Transform the system of equations into its ... more

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 , ; Transform the system of equations into its ... more

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 ,  ; Transform the system of equations into its ... more

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, ; Transform the system of equations into its ... more

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, , ; Transform the system of equations into its ... more

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, , ; Transform the system of equations into its ... more

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, , ; Transform the system of equations into its ... more

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, , , ; Transform the system of equations into its... more

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, , ; Transform the system of equations into its ... more

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, , ; Transform the system of equations into its ... more

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, , ; Transform the system of equations into its ... more

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, , ; Transform the system of equations into its ... more

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, , , ; Transform the system of equations into its... more

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, , , ; Transform the system of equations into its... more

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; Rewrite the matrix equation as   where is the... more

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; Rewrite the matrix equation as   where is the... more

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; Find the inverse of using the rule for finding... more

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; Let be the given matrix. Set up the matrix... more

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The inverse does not exist for . ; Find the ... more

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 The inverse exists for any real number x. ; Find ... more

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 The inverse exists for any real number x. ; Let ... more

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 The inverse does not exist for and ; Find the ... more

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No. The inverse of the matrix does not exist ... more

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, ; Construct matrices and such that . These ... more

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Only square matrices have determinants. ; Only ... more

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The determinant of any square matrix is a real ... more

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Only square matrices with nonzero determinants are... more

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6 ; Find the determinant of the given matrix using... more

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2 ; Find the determinant of the given matrix using... more

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0 ; Find the determinant of the given matrix using... more

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0 ; Find the determinant of the given matrix using... more

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; Note that the determinant of a matrix is ... more

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1 ; Note that the determinant of a matrix is ... more

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does not exist ; Determine the dimension of the ... more

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does not exist ; Determine the dimension of the ... more

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; Note that the determinant of a matrix is ... more

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2.9 ; Note that the determinant of a matrix is ... more

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; Note that the determinant of a matrix is ... more

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; Note that the determinant of a matrix is ... more

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; Note that the determinant of a matrix is ... more

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; Note that the determinant of a matrix is ... more

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; Note that the determinant of a matrix is ... more

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; Note that the determinant of a matrix is ... more

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Determinant: 4The matrix has an inverse. ; Let ... more

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Determinant: 0The matrix does not have an inverse... more

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Determinant: 5000The matrix has an inverse. ; Let... more

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Determinant: The matrix has an inverse. ; Let and... more

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Determinant: 0The matrix does not have an inverse... more

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Determinant: 2The matrix has an inverse. ; Let ... more

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Determinant: The matrix has an inverse. ; Let and... more

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Determinant: 92The matrix has an inverse. ; Let ... more

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Determinant: The matrix has an inverse. ; Find the... more

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Determinant: 1080The matrix has an inverse. ; Find... more

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Determinant: The matrix has an inverse. ; Find the... more

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Determinant: 0The matrix does not have an inverse... more

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Determinant: 0The matrix does not have an inverse... more

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Determinant: The matrix has an inverse. ; Find the... more

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; Let be the corresponding matrix of the given ... more

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; Let be the corresponding matrix of the given ... more

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120 ; Let be the corresponding matrix of the ... more

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32 ; Let be the corresponding matrix of the given... more

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1024 ; Let be a matrix whose nondiagonal entries... more

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; The goal is to find and , where and .Start by... more

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; The goal is to find and , where and .Start by... more

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; The goal is to find and , where and .Start by... more

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; The goal is to find and , where and .Start by... more

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; The goal is to find and , where and .Start by... more

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; The goal is to find and , where and .Start by... more

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; The goal is to find , , and , where , , and .... more

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; The goal is to find , , and , where , , and .... more

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; The goal is to find , , and , where , , and .... more

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; The goal is to find , , and , where , , and .... more

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; The goal is to find , , and , where , , and .... more

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; The goal is to find , , and , where , , and .... more

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; The goal is to find , , and , where , , and .... more

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; The goal is to find , , and , where , , and .... more

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; The goal is to find the solution , where , , , ... more

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; The goal is to find the solution , where , , , ... more

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Area: 21 ; Plot the vertices on the -plane. Then ... more

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Area: ; Plot the vertices on the -plane. Then ... more

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Area: ; Plot the vertices on the -plane. Then ... more

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Area: 33 ; Plot the vertices on the -plane. Then ... more

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; Let be the corresponding matrix of the given ... more

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; Let be the corresponding matrix of the given ... more

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0, 1, 2 ; Let be the corresponding matrix of the ... more

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1 ; Evaluate using expansion of the determinant ... more

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, ; Evaluate using expansion of the determinant ... more

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, ; Evaluate using expansion of the determinant ... more

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Consider the matrix .Denote rows 1, 2, and 3 by... more

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; From the given graph, determine the vertices of... more

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Gaussian elimination is preferable since ... more

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An matrix A has number of rows and number of ... more

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A matrix is in row-echelon form when the following... more

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Exactly one solution:  All the variables in the ... more

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The reduced row-echelon form of a matrix is in row... more

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Add the corresponding entries of and to find , ... more

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0 ; Since the given matrix is a square matrix of ... more

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0 ; As the given matrix is a square matrix of ... more

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; As the given matrix is a square matrix of order... more

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1 ; As the given matrix is a square matrix of ... more

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Does not exist ; Since the given matrix is not a ... more

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Does not exist ; Since the given matrix is not a ... more

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; As the given matrix is a square matrix of order... more

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; As the given matrix is a square matrix of order... more

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20; 20 ; To find , delete the first row and the ... more

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5; 5 ; To find , delete the third row and the ... more

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

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0; 0 ; To find , delete the first row and the ... more

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0; 0 ; To find , delete the second row and the ... more

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; To find , delete the third row and the second ... more

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4; The matrix has an inverse. ; Since the given ... more

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0; the matrix does not have an inverse. ; Since ... more

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Impossible, the order of matrices are different... more

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; Substitute the matrices C and D. ; Subtract the... more

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; Substitute the matrices C and D. ; Multiply the... more

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Impossible, the order of matrices are different... more

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; Substitute the matrices G and A. ; Multiply 5 ... more

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Not possible. Number of rows of the matrix A is ... more

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; Substitute the matrices B and C. ; Multiply the... more

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; Substitute the matrices C and B. ; Multiply ... more

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; Substitute the values of the matrices B and F... more

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; Substitute the matrices F and C. ; Multiply ... more

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; Perform the matrix addition C+D. ; Perform the ... more

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; Perform the matrix subtraction 2C-D.  Multiply ... more

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; The determinant of a matrix remains same after ... more

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; The determinant of a matrix remains same after ... more

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120 ; The determinant of a matrix remains same ... more

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32 ; The determinant of a matrix remains same ... more

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; Use CAS to calculate the value of . ; Use CAS ... more

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; Use CAS to calculate the value of . ; Use CAS ... more

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; Use CAS to calculate the value of . ; Use CAS ... more

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; Use CAS to calculate the value of . ; ... more

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; Use the MATRIX feature in the CAS to enter .Use... more

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; Use the MATRIX feature in the CAS to enter the ... more

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  AB=BA=IHence the matrices are inverses of each ... more

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 AB=BA=IThis proves that A and B are the inverse ... more

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; Solve the matrix equation for X. ; Substitute ... more

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; Solve the matrix equation for . ; Substitute ... more

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; Solve the matrix equation for . ; Substitute ... more

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 No solution ; Solve the matrix equation for . ; ... more

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; Solve the matrix equation for . ; Find the ... more

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; Solve the matrix equation for . ; Find the ... more

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1; ; Find the determinant of the matrix using ... more

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, ; Find the determinant of the matrix by cross ... more

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0, no inverse ; Find the determinant by cross ... more

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0; no inverse ;  Find the determinant of the ... more

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-1; ; Find the determinant of the matrix using the... more

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3; ; Find the determinant of the matrix using the ... more

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24; ; Find the determinant of the matrix using the... more

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0; no inverse ; Calculate the determinant of the ... more

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; Write the equation in the matrix form. ; ... more

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; Write the equation in the matrix form. ; ... more

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; Write the equation in matrix form. ; Substitute... more

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; Write the equation in matrix form. ; Substitute... more

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; To find the solution to the system of equations... more

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; To find the solution to the system of equations... more

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; To find the solution to the system of equations... more

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; Find , , and , where , , and .Start by writing ... more

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11 ; Use the given graph to determine the vertices... more

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; Use the given graph to determine the vertices ... more

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; Let x, y and z denote the amounts in the ... more

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; Let , and be the quantity in lb of type H, S... more

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Leading entry of each row is 1. The leading entry ... more

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

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No solution ; Write the augmented matrix of the ... more

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

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; Determine the corresponding augmented matrix of... more

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Incompatible dimensions ; The dimension of a ... more

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Incompatible dimensions ; The dimension of a ... more

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

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; In order to perform matrix multiplication, the ... more

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; Use the formula, to calculate the value of ... more

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Does not exist. ; A matrix will have an inverse ... more

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Does not exist. ; The determinant of any matrix ... more

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; Expand the matrix by the first row to ... more

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Since the determinant of matrix is 0, does not ... more

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; The Cramer's rule is applied to solve the ... more

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Item A: lb; Item W: lb ; Assume the quantity of ... more

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The grey matrix is a square with matrix, .... more

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The grey matrix is a square with matrix, .... more

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