Consider the following Gauss-Jordan reduction: 1 01 ΓΟ 1 0 [0 1 07 [1 ⠀⠀⠀⠀⠀ 1 03 0 0 1 E₂E₂A 9 2 27 001 A 9 0 27 00 1 E₁A 3 0 1 0 001 E₂E₂E₁ A [1 0 1 0 001 E₁E₂E₂E₁ A = I

Algebra and Trigonometry (6th Edition)
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ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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Consider the following Gauss-Jordan reduction:
Find
E₁ =
E₁
=
ΤΟ 1 01 ΤΟ 1 0 50 1 07 [1 0 37 [1 0 01
103
⠀⠀⠀⠀⠀
0 0 1
Ę₂Ę₂ A
[01 0
9 2 27 =
0 0 1
9 2 27 → 9 0 27
0 0 1
A
001
E₁A
, E₂ =
-1 1
Write A as a product A = E₁¹E₂¹E¹E¹ of elementary matrices:
0 1 0
0 0 1
E₂E¹₂E₂ A
E3 =
010
0 0 1
E₁E₂E₂E₁ A
= I
Transcribed Image Text:Consider the following Gauss-Jordan reduction: Find E₁ = E₁ = ΤΟ 1 01 ΤΟ 1 0 50 1 07 [1 0 37 [1 0 01 103 ⠀⠀⠀⠀⠀ 0 0 1 Ę₂Ę₂ A [01 0 9 2 27 = 0 0 1 9 2 27 → 9 0 27 0 0 1 A 001 E₁A , E₂ = -1 1 Write A as a product A = E₁¹E₂¹E¹E¹ of elementary matrices: 0 1 0 0 0 1 E₂E¹₂E₂ A E3 = 010 0 0 1 E₁E₂E₂E₁ A = I
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