Consider the following Gauss-Jordan reduction Find B₁ = 0 1 27 -7 -3 0 1 0 27 -7-3 - 1 0 1 Write A as a product A=E, ¹E, ¹E, ¹E, of elementary matrices -7 0 0 0 E₁A 4 16884-888-8834838 =======||===||=== 1 0 17 -7 0 0 0 E₂E.A Го 1 [100] ED 01 0 0 1 0 I 10 0 001 F₂₂₁A EE₂₂A
Consider the following Gauss-Jordan reduction Find B₁ = 0 1 27 -7 -3 0 1 0 27 -7-3 - 1 0 1 Write A as a product A=E, ¹E, ¹E, ¹E, of elementary matrices -7 0 0 0 E₁A 4 16884-888-8834838 =======||===||=== 1 0 17 -7 0 0 0 E₂E.A Го 1 [100] ED 01 0 0 1 0 I 10 0 001 F₂₂₁A EE₂₂A
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:Consider the following Gauss-Jordan reduction: Find E₁ = -9 27 1-9 0 1 27-7-3=10001-7-300E₂A-9011 Write A
as a product A = E¹E¹E¹E¹ of elementary matrices: 0 11 00-70 E,A >> 010-70 E₂,E,A 0 0 1 0 0 0 1 0 E₂ E₂ E, AO →
HEACHEE+BEEHB E3 = 00 01 EEE₂E₁A = | E4=
Consider the following Gauss-Jordan reduction
Find
9
27
1
0
-7
0
-9 0
27 -7
1 0
A
1
-3
0
-
1
Write A as a product A=E, ¹E, ¹E, ¹E, of elementary matrices
7 00
E₁A
0
0
-7 0 001
100
E₂E₁A
0
0
100
₂₂A
n
00
010-I
MESEMBEEHEEEHEEE
==
001
EEEEA
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Step 1: Write the three type elementary matrices and their inverses
VIEWStep 2: Use elementary row operations on A
VIEWStep 3: Write the given Gauss Jordan reduction of A
VIEWStep 4: Determine the elementary matrices E1 , E2 ,E3 ,E4
VIEWStep 5: Determine the inverse of the required elementary matrices
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