Explanation Given information: The provided matrix A is [ 1 2 5 2 3 8 − 1 1 2 ] . Formula Used: Let A be an n × n matrix. Step 1: From the n × 2 n augmented matrix [ A | I ] , where I is the n × n identity matrix. Step 2: If there is a sequence of elementary row operation that transform A into I, then this same sequence of row operation will transform [ A | I ] into [ I | B ] , where B = A − 1 . Step 3: Check your work by showing that A A − 1 = I . Proof: Start by adjoining the identity matrix I = [ 1 0 0 0 1 0 0 0 1 ] so the matrix A to form the augmented matrix [ A | I ] . [ A | I ] = [ 1 2 5 2 3 8 − 1 1 2 | 1 0 0 0 1 0 0 0 1 ] Now, perform row operation on [ A | I ] to transform it to a matrix of the form [ I | B ] . [ 1 2 5 2 3 8 − 1 1 2 | 1 0 0 0 1 0 0 0 1 ] → R 3 + R 1 → R 3 R 2 − 2 R 1 → R 2 [ 1 2 5 0 − 1 − 2 0 3 7 | 1 0 0 − 2 1 0 1 0 1 ] Again, we have to perform the row operation R 1 + 2 R 2 → R 1 and R 3 + 3 R 2 → R 3

3rd Edition

ISBN: 9780321912787

Author: Ratti, J. S., Mcwaters, Marcus

Publisher: Pearson,

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Every field in the present world involves a set. The theory of sets was developed by German mathematician Georg Cantor while working on the “problems of trigonometric series”.

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Chapter 6.3, Problem 41E

To determine

To Prove:

The inverse of A is [2−1−112−7−2−531].

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Chapter 6.3, Problem 40E

Chapter 6.3, Problem 42E

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To Prove: The inverse of A is [ 2 − 1 − 1 12 − 7 − 2 − 5 3 1 ] .

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To Prove: The inverse of A is [2−1−112−7−2−531].

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Chapter 6 Solutions

To Prove:

The inverse of A is [2−1−112−7−2−531].