Explanation Given Information: The matrix is, A = [ 2 − 9 1 − 4 ] B = [ 9 5 7 4 ] Formula Used: The inverse of matrix A = [ a b c d ] , A − 1 = 1 a d − b c [ d − c − d a ] Also, the relation between the inverse multiplications of two matrices. ( A B ) − 1 = B − 1 A − 1 Calculation: Consider the given matrix A = [ 2 − 9 1 − 4 ] , B = [ 9 5 7 4 ] . [ A B ] = [ 2 − 9 1 − 4 ] [ 9 5 7 4 ] = [ 18 − 63 10 − 36 9 − 16 5 − 16 ] = [ − 45 − 26 − 19 − 11 ] Now, The inverse of matrix [ A B ] is equal to A B − 1 = 1 a d − b c [ d − b − c a ] . Now, we will compare the matrix to the original matrix. So, a = − 45 b = − 26 c = − 19 d = − 11 Now, the inverse is: A − 1 = 1 a d − b c [ d − b − c a ] Substitutes the values to get, A − 1 = 1 a d − b c [ d − b − c a ] = 1 − 1 [ − 11 26 19 − 45 ] = [ − 11 26 19 − 45 ] Therefore, the inverse of the matrix [ A B ] is [ − 11 26 19 − 45 ]

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ISBN: 9780134469140

Author: Robert F. Blitzer

Publisher: PEARSON

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Chapter 8.4, Problem 48PE

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To calculate: The inverse of the matrix (AB)−1,A−1B−1,B−1A−1 where A=[2−91−4],B=[9574].

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Chapter 8.4, Problem 47PE

Chapter 8.4, Problem 49PE

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Ch. 8.1 - Check Point 1 Write the augmented matrix for the...Ch. 8.1 - Check Point 2 Use the matrix ...Ch. 8.1 - Check Point 3 Use matrices to solve the system:...Ch. 8.1 - Check Point 4 Use matrices to solve the system:...Ch. 8.1 - Check Point 5 Solve the system in Check Point. 3...Ch. 8.1 - Prob. 1CVC Ch. 8.1 - Fill in each blank so that the resulting statement...Ch. 8.1 - Prob. 3CVC Ch. 8.1 - Prob. 4CVC Ch. 8.1 - Fill in each blank so that the resulting statement...

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The inverse of the matrix ( A B ) − 1 , A − 1 B − 1 , B − 1 A − 1 where A = [ 2 − 9 1 − 4 ] , B = [ 9 5 7 4 ] .

Solution Summary: The author calculates the inverse of the matrix (AB)-1,A1,B1 and the relation between the two matrices.

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To calculate: The inverse of the matrix (AB)−1,A−1B−1,B−1A−1 where A=[2−91−4],B=[9574].

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Chapter 8 Solutions