Explanation Given Information: The matrix A = [ 1 − 2 1 0 0 1 − 2 1 0 0 1 − 2 0 0 0 1 ] , B = [ 1 2 3 4 0 1 2 3 0 0 1 2 0 0 0 1 ] 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 = [ 1 − 2 1 0 0 1 − 2 1 0 0 1 − 2 0 0 0 1 ] , B = [ 1 2 3 4 0 1 2 3 0 0 1 2 0 0 0 1 ] Now, we will compute the matrix as [ A B ] A B = [ 1 − 2 1 0 0 1 − 2 1 0 0 1 − 2 0 0 0 1 ] [ 1 2 3 4 0 1 2 3 0 0 1 2 0 0 0 1 ] = [ 1 × 0 + ( − 2 ) × 0 + 1 × 0 + 0 × 0 1 × 2 + ( − 2 ) × 1 + 1 × 0 + 0 × 0 1 × 3 + ( − 2 ) × 2 + 1 × 1 + 0 × 0 1 × 4 + ( − 2 ) × 3 + 1 × 2 + 0 × 1 0 × 0 + 1 × 0 + ( − 2 ) × 0 + 1 × 0 0 × 2 + 1 × 1 + ( − 2 ) × 0 + 1 × 0 0 × 3 + 1 × 2 + ( − 2 ) × 1 + 1 × 0 0 × 4 + 1 × 3 + ( − 2 ) × 2 + 1 × 1 0 × 0 + 0 × 0 + 1 × 0 + ( − 2 ) × 0 0 × 2 + 0 × 1 + 1 × 0 + ( − 2 ) × 0 0 × 3 + 0 × 2 + 1 × 1 + ( − 2 ) × 0 0 × 4 + 0 × 3 + 1 × 2 + ( − 2 ) × 1 0 × 0 + 0 × 0 + 0 × 0 + 1 × 0 0 × 2 + 0 × 1 + 0 × 0 + 1 × 0 0 × 3 + 0 × 2 + 0 × 1 + 1 × 0 0 × 4 + 0 × 3 + 0 × 2 + 1 × 1 ] = [ 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 ] = I 4 Now, we will compute the matrix as [ B A ] B A = [ 1 2 3 4 0 1 2 3 0 0 1 2 0 0 0 1 ] [ 1 − 2 1 0 0 1 − 2 1 0 0 1 − 2 0 0 0 1 ] = [ 1 × 1 + 2 × 0 + 3 × 0 + 4 × 0 1 × ( − 2 ) + 2 × 1 + 3 × 0 + 4 × 0 1 ×

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Author: Robert F. Blitzer

Publisher: PEARSON

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Chapter 8.4, Problem 12PE

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To calculate: The product of the matrix AB, BA where, A=[1−21001−21001−20001],B=[1234012300120001] and also find the matrix B is the Multiplicative inverse of matrix A.

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Chapter 8.4, Problem 11PE

Chapter 8.4, Problem 13PE

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Chapter 8 Solutions

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 = [ 1 − 2 1 0 0 1 − 2 1 0 0 1 − 2 0 0 0 1 ] , B = [ 1 2 3 4 0 1 2 3 0 0 1 2 0 0 0 1 ] and also find the matrix B is the Multiplicative inverse of matrix A .

Solution Summary: The author explains that 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=[1−21001−21001−20001],B=[1234012300120001] and also find the matrix B is the Multiplicative inverse of matrix A.

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Chapter 8 Solutions