Consider the following Gauss elimination: Γ1 0 07 A 0 1 0A0 -30E₁A→ 0 1 0 E₂E₁A →→ ⠀⠀⠀⠀⠀⠀ 004 E [105] 0 0 1 E₁ What is the determinant of A? det (A) = [1 0 01 0 0 1 E₂ [100] 0 0 1 E3E₂E₁A = 0 1 0 E [8 04

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
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Chapter4: Eigenvalues And Eigenvectors
Section4.2: Determinants
Problem 52EQ: In Exercises 47-52, assume that A and B are nn matrices with det A = 3 and det B=2. Find the...
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Consider the following Gauss elimination:
[100]
A →→ 0 1 0 A → 0 -30E₁A → 0 1 0 E₂E₁A → 0 0 1 E3E₂E₁A
⠀⠀⠀⠀⠀⠀⠀
004
E₂
[10 57
001
E₁
What is the determinant of A?
det (A) =
[1 0 01
0 0 1
E₂
[100]
0 1 0
E₁
[8
0
5
4
47
008
Transcribed Image Text:Consider the following Gauss elimination: [100] A →→ 0 1 0 A → 0 -30E₁A → 0 1 0 E₂E₁A → 0 0 1 E3E₂E₁A ⠀⠀⠀⠀⠀⠀⠀ 004 E₂ [10 57 001 E₁ What is the determinant of A? det (A) = [1 0 01 0 0 1 E₂ [100] 0 1 0 E₁ [8 0 5 4 47 008
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