Explanation Given Information: The matrix A = [ − 2 1 − 1 − 5 2 − 1 3 − 1 1 ] , B = [ 1 0 1 2 1 3 − 1 1 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 provided expression is A = [ − 2 1 − 1 − 5 2 − 1 3 − 1 1 ] , B = [ 1 0 1 2 1 3 − 1 1 1 ] Now, we will compute the matrix as [ A B ] A B = [ − 2 1 − 1 − 5 2 − 1 3 − 1 1 ] [ 1 0 1 2 1 3 − 1 1 1 ] = [ ( − 2 ) × 1 + 1 × 2 + ( − 1 ) × ( − 1 ) ( − 2 ) × 0 + 1 × 1 + ( − 1 ) × 1 ( − 2 ) × 1 + 1 × 3 + ( − 1 ) × 1 ( − 5 ) × 1 + 2 × 2 + ( − 1 ) × ( − 1 ) ( − 5 ) × 0 + 2 × 1 + ( − 1 ) × 1 ( − 5 ) × 1 + 2 × 3 + ( − 1 ) × 1 3 × 1 + ( − 1 ) × 2 + 1 × ( − 1 ) 3 × 0 + ( − 1 ) × 1 + 1 × 1 3 × 1 + ( − 1 ) × 3 + 1 × 1 ] = [ 1 0 0 0 1 0 0 0 1 ] = I 3 Now, we will compute the matrix as [ B A ] B A = [ 1 0 1 2 1 3 − 1 1 1 ] [ − 2 1 − 1 − 5 2 − 1 3 − 1 1 ] = [ 1 × ( − 2 ) + 0 × ( − 5 ) + 1 × 3 1 × 1 + 0 × 2 + 1 × ( − 1 ) 1 × ( − 1 ) + 0 × ( − 1 ) + 1 × 1 2 × ( − 2 ) + 1 × ( − 5 ) + 3 × 3 2 × 1 + 1 × 2 + 3 × ( − 1 ) 2 × ( − 1 ) + 1 × ( − 1 ) + 3 × 1 ( − 1 ) × ( − 2 ) + 1 × ( − 5 ) + 1 × 3 ( − 1 ) × 1 + 1 × 2 + 1 × ( − 1 ) ( − 1 ) × ( − 1 ) + 1 × ( − 1 ) + 1 × 1 ] = [ 1 0 0 0 1 0 0 0 1 ] = I 3 Since both matrix A B and matrix B A are equal to the the identity matrix Now, we will compute the matrix B = A − 1

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Author: Blitzer

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Chapter 8.4, Problem 8PE

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To calculate: The product of the matrix AB, BA where, A=[−21−1−52−13−11],B=[101213−111] and also find the matrix B is the multiplicative inverse of matrix A.

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The product of the matrix A B , B A where, A = [ − 2 1 − 1 − 5 2 − 1 3 − 1 1 ] , B = [ 1 0 1 2 1 3 − 1 1 1 ] and also find the matrix B is the multiplicative inverse of matrix A .

Solution Summary: The author calculates 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=[−21−1−52−13−11],B=[101213−111] and also find the matrix B is the multiplicative inverse of matrix A.

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Chapter 8 Solutions