We can find the inverse of a matrix by row reduction. Suppose matrix A is given and we wish to find dj1 d12 a13 bu h2 13 (1 0 0` its inverse B = A". Then, AB = E or | a21 a2 a23 || b1 bz2 b3 =| 0 1 0 0 0 1 a31 a32 A33 b31 b32 b33 a13 1 0 0 Form the augmented matrix a21 an az3 0 1 0 and carry out row reduction so that the left аз1 аз2 а33 00 1 ´1 0 0 bu b2 b13 0 b21 b2 b23 |. The 0 0 1 b31 b32 b33, hand side of the augmented matrix becomes a 3 × 3 identity matrix, 0 required matrix is the matrix remaining on the right hand side. ´-1 8 -2 Use this procedure to find the inverse of A =| -6 49 -10 -4 34 - 5

We can find the inverse of a matrix by row reduction. Suppose matrix A is given and we wish to find dj1 d12 a13 bu h2 13 (1 0 0` its inverse B = A". Then, AB = E or | a21 a2 a23 || b1 bz2 b3 =| 0 1 0 0 0 1 a31 a32 A33 b31 b32 b33 a13 1 0 0 Form the augmented matrix a21 an az3 0 1 0 and carry out row reduction so that the left аз1 аз2 а33 00 1 ´1 0 0 bu b2 b13 0 b21 b2 b23 |. The 0 0 1 b31 b32 b33, hand side of the augmented matrix becomes a 3 × 3 identity matrix, 0 required matrix is the matrix remaining on the right hand side. ´-1 8 -2 Use this procedure to find the inverse of A =| -6 49 -10 -4 34 - 5

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter2: Systems Of Linear Equations

Section2.2: Direct Methods For Solving Linear Systems

Problem 22EQ: Consider the matrix A=[2314]. Show that any of the three types of elementary row operations can be...

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Similar questions

Show that no 22 matrices A and B exist that satisfy the matrix equation. AB-BA=1001.
Use an example chosen from 22 matrices to show that for nn matrices A and B,ABBA but AB=BA.
Consider the matrix A=[2314]. Show that any of the three types of elementary row operations can be used to create a leading 1 at the top of the first column. Which do you prefer and why?

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