It is given that E4E3E2E1A=⎡⎣⎢⎢⎢−1002−40488⎤⎦⎥⎥⎥.Here the matrices E4, E3, E2, and, E1 are:E1=⎡⎣⎢⎢⎢100010008⎤⎦⎥⎥⎥E2=⎡⎣⎢⎢⎢100010−501⎤⎦⎥⎥⎥E3=⎡⎣⎢⎢⎢1000−10001⎤⎦⎥⎥⎥E4=⎡⎣⎢⎢⎢001010100⎤⎦⎥⎥⎥ Consider the following Gauss elimination:[100][1 0 010 5A->001 A→A0 0 1 0 E₁A →[010]0060 1 0 E2E₁A →[001]E1E2E3What is the determinant of A?1 0 0090 E3E2E₁A =0 0 1E44 -2 -2== 0-1 80 03

Answered: Image /qna-images/answer/c62e8b64-b459-41e3-8b8d-7045302cd4f6.jpg

Consider the following Gauss elimination: [100] [1 0 0 10 5 A-> 001 A→ A0 0 1 0 E₁A → [010] 006 0 1 0 E2E₁A → [001] E1 E2 E3 What is the determinant of A? 1 0 0 090 E3E2E₁A = 0 0 1 E4 4 -2 -2 == 0-1 8 0 0 3

Consider the following Gauss elimination: [100] [1 0 0 10 5 A-> 001 A→ A0 0 1 0 E₁A → [010] 006 0 1 0 E2E₁A → [001] E1 E2 E3 What is the determinant of A? 1 0 0 090 E3E2E₁A = 0 0 1 E4 4 -2 -2 == 0-1 8 0 0 3

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter9: Systems Of Equations And Inequalities

Section9.8: Determinants

Problem 25E

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Question

It is given that E4E3E2E1A=⎡⎣⎢⎢⎢−1002−40488⎤⎦⎥⎥⎥.

Here the matrices E4, E3, E2, and, E1 are:

E1=⎡⎣⎢⎢⎢100010008⎤⎦⎥⎥⎥E2=⎡⎣⎢⎢⎢100010−501⎤⎦⎥⎥⎥E3=⎡⎣⎢⎢⎢1000−10001⎤⎦⎥⎥⎥E4=⎡⎣⎢⎢⎢001010100⎤⎦⎥⎥⎥

Consider the following Gauss elimination:
[100]
[1 0 0
10 5
A->
001 A→
A0 0 1 0 E₁A →
[010]
006
0 1 0 E2E₁A →
[001]
E1
E2
E3
What is the determinant of A?
1 0 0
090 E3E2E₁A =
0 0 1
E4
4 -2 -2
== 0-1 8
0 0
3

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