Explanation Given Information: The expression is A = [ 2 0 0 0 4 0 0 0 6 ] Formula used: To find A − 1 , first form [ A | I ] then use row operation to obtain [ I | B ] that indicates B = A − 1 . Calculation: Consider the given matrix A = [ 2 0 0 0 4 0 0 0 6 ] Augment with identity matrix: [ A | I ] = [ 2 0 0 1 0 0 0 4 0 0 1 0 0 0 6 0 0 1 ] Now, we will use following row operations to row reduces for inverse: R 3 → 1 6 × R 3 , R 2 → 1 4 × R 2 , R 1 → 1 2 × R 1 The resulting matrix is: [ A | I ] = [ 1 0 0 1 2 0 0 0 1 0 0 1 4 0 0 0 1 0 0 1 6 ] = [ I | B ] So, the inverse of matrix is: A − 1 = [ 1 2 0 0 0 1 4 0 0 0 1 6 ] Where B = A − 1 Now, check the result for A A − 1 = I 3 And A − 1 A = I 3 Here, A = [ 2 0 0 0 4 0 0 0 6 ] Now, A A − 1 = [ 2 0 0 0 4 0 0 0 6 ] [ 1 2 0 0 0 1 4 0 0 0 1 6 ] A A

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Author: Blitzer

Publisher: PEARSON

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In mathematics, problems can be solved by the arithmetic operators like addition, subtraction, multiplication, and division. In algebra, we represent the numbers by any letter called a variable. If these variables are of degree 1, then it is studied unde…

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Chapter 8.4, Problem 19PE

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To calculate: The inverse of matrix A=[200040006] and also check the result.

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Chapter 8 Solutions

EBK PRECALCULUS

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The inverse of matrix A = [ 2 0 0 0 4 0 0 0 6 ] and also check the result.

Solution Summary: The author explains how to calculate the inverse of the matrix A=left and check the result.

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