College Algebra (6th Edition)

Published by Pearson
ISBN 10: 0-32178-228-3
ISBN 13: 978-0-32178-228-1

Chapter 6 - Matrices and Determinants - Exercise Set 6.4 - Page 640: 59

Answer

Procedure: 1. Form the augmented matrix $[A|I_{n}]$ 2. Perform row operations on $[A|I_{n}]$ to obtain a matrix of the form $[I_{n}|B]$ 3. Matrix $B$ is $A^{-1}$.

Work Step by Step

If the matrix A is n$\times$n where $n > 2$, use the procedure outlined on p.634: To find $A^{-1}$ for any $n\times n$ matrix $A$ for which $A^{-1}$ exists, 1. Form the augmented matrix $[A|I_{n}]$ 2. Perform row operations on $[A|I_{n}]$ to obtain a matrix of the form $[I_{n}|B]$ 3. Matrix $B$ is $A^{-1}$.
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