Explanation Given Information: The matrix A = [ 0 0 − 2 1 − 1 0 1 1 0 1 − 1 0 1 0 0 − 1 ] , B = [ 1 2 0 3 0 1 1 1 0 1 0 1 1 2 0 2 ] Formula used: To find A − 1 , first form [ A | I ] then use row operation to obtain [ I | B ] that indicates B = A − 1 . Calculation: The given expression is A = [ 0 0 − 2 1 − 1 0 1 1 0 1 − 1 0 1 0 0 − 1 ] , B = [ 1 2 0 3 0 1 1 1 0 1 0 1 1 2 0 2 ] Now we will compute the matrix as [ A B ] A B = [ 0 0 − 2 1 − 1 0 1 1 0 1 − 1 0 1 0 0 − 1 ] [ 1 2 0 3 0 1 1 1 0 1 0 1 1 2 0 2 ] = [ 0 × 1 + 0 × 0 + ( − 2 ) × 0 + 1 × 1 0 × 2 + 0 × 1 + ( − 2 ) × 1 + 1 × 2 0 × 0 + 0 × 1 + ( − 2 ) × 1 + 1 × 0 0 × 3 + 0 × 1 + ( − 2 ) × 1 + 1 × 2 ( − 1 ) × 1 + 0 × 0 + 1 × 0 + 1 × 1 ( − 1 ) × 2 + 0 × 1 + 1 × 1 + 1 × 2 ( − 1 ) × 0 + 0 × 1 + 1 × 0 + 1 × 0 ( − 1 ) × 3 + 0 × 1 + 1 × 1 + 1 × 2 0 × 1 + 1 × 0 + ( − 1 ) × 0 + 0 × 1 0 × 2 + 1 × 1 + ( − 1 ) × 1 + 0 × 2 0 × 0 + 1 × 1 + ( − 1 ) × 0 + 0 × 0 0 × 3 + 1 × 1 + ( − 1 ) × 1 + 0 × 2 1 × 1 + 0 × 0 + 0 × 0 + ( − 1 ) × 1 1 × 2 + 0 × 1 + 0 × 1 + ( − 1 ) × 2 1 × 0 + 0 × 1 + 0 × 0 + ( − 1 ) × 0 1 × 3 + 0 × 1 + 0 × 1 + ( − 1 ) × 2 ] = [ 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 ] = I 4 And by computing the matrix as [ B A ] we get, B A = [ 1 2 0 3 0 1 1 1 0 1 0 1 1 2 0 2 ] [ 0 0 − 2 1 − 1 0 1 1 0 1 − 1 0 1 0 0 − 1 ] = [ 1 × 0 + 2 × ( − 1 ) + 0 × 0 + 3 × 1 1 × 0 + 2 × 0 + 0 × 1 + 3 × 0 1 × ( − 2 ) + 2 × 1 + 0 × ( − 1 ) + 3 × 0 1 × 1 + 2 × 1 + 0 × 0 + 3 × ( − 1 ) 0 × 0 + 1 × ( − 1 ) + 1 × 0 + 1 × 1

MyLab Math with Pearson eText -- Standalone Access Card -- for Precalculus (6th Edition)

6th Edition

ISBN: 9780134757834

Author: Robert F. Blitzer

Publisher: PEARSON

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Chapter 8.4, Problem 11PE

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To calculate: The product of the matrix AB, BA where, A=[00−21−101101−10100−1],B=[1203011101011202] and also find the whether matrix B is the multiplicative inverse of matrix A.

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Chapter 8.4, Problem 10PE

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MyLab Math with Pearson eText -- Standalone Access Card -- for Precalculus (6th Edition)

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 product of the matrix A B , B A where, A = [ 0 0 − 2 1 − 1 0 1 1 0 1 − 1 0 1 0 0 − 1 ] , B = [ 1 2 0 3 0 1 1 1 0 1 0 1 1 2 0 2 ] and also find the whether matrix B is the multiplicative inverse of matrix A .

Solution Summary: The author calculates the product of the matrix AB, BA and B is the multiplicative inverse of A.

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To calculate: The product of the matrix AB, BA where, A=[00−21−101101−10100−1],B=[1203011101011202] and also find the whether matrix B is the multiplicative inverse of matrix A.

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Chapter 8 Solutions