Express the matrix and its inverse as products of elementary matrices. A=[1,0,−2; 0,4,3; 0,0,1] H~~~~~~ The matrix A can be written as:EEB10 0T1 0 0Ţi 0 00 1 0A-10 4 00 1 00 0 112! 0 11 00[1 00 T1 0 20 1 00 0 1A-0 1 -30 00 011 0 01 01A-!0 1 00 3 140 1 00 0-10 110010 0T1 0 2A-10 4 00 1 30 0 10 1 00 0 11 0 00 0 11 010 0A-10 11 -20 10 1 00 010 01 The matrix A can be written as:O[1 0 21 010 00 1 00 1-30 4 00 0 10 0 10 01 0-1 0 1O[1 0 20 0111 0 010 1 30 -4 020 1111 000 1 00 0 11 010 4 00 0 11 0 0-3 11 0 00 1 3-20 4 00 0 10 10 010 0 1O[1 00 1 02 0 11 010 130 -4 00 0 11

Given matrix, A=10-2043001 The objective is to express the matrix and its inverse as products of…

Answered: Express the matrix and its inverse as…

Math

Algebra

Express the matrix and its inverse as products of elementary matrices. A=[1,0,−2; 0,4,3; 0,0,1]

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter3: Matrices

Section3.5: Subspaces, Basis, Dimension, And Rank

Problem 15EQ

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Question

Express the matrix and its inverse as products of elementary matrices.

A=[1,0,−2; 0,4,3; 0,0,1]

H~~~~~~

The matrix A can be written as:
EEB
10 0T1 0 0Ţi 0 0
0 1 0
A-1
0 4 0
0 1 0
0 0 1
1
2
! 0 1
1 0
0[1 0
0 T1 0 2
0 1 0
0 0 1
A-
0 1 -3
0 0
0 0
1
1 0 0
1 0
1
A-!
0 1 0
0 3 1
4
0 1 0
0 0
-1
0 1
100
10 0T1 0 2
A-1
0 4 0
0 1 3
0 0 1
0 1 0
0 0 1
1 0 0
0 0 1
1 0
1
0 0
A-1
0 1
1 -
20 1
0 1 0
0 0
1
0 0
1

The matrix A can be written as:
O[1 0 2
1 0
10 0
0 1 0
0 1
-3
0 4 0
0 0 1
0 0 1
0 0
1 0
-1 0 1
O[1 0 2
0 0
1
1
1 0 0
1
0 1 3
0 -4 0
20 1
1
1
1 00
0 1 0
0 0 1
1 0
1
0 4 0
0 0 1
1 0 0
-3 1
1 0 0
0 1 3
-2
0 4 0
0 0 1
0 1
0 0
1
0 0 1
O[1 0
0 1 0
2 0 1
1 0
1
0 1
3
0 -4 0
0 0 1
1

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