(b) Let 1 E₁ = -2 - 0 0 0 1 0 01 E₂ = 1 0 -3 Compute Y = E3E2E1 and its inverse Y-1. Compute Z = E1 E2 E3 and its inverse Z-¹. 00 10 0 1 E3 = 1 0 0 0 1 0 0-4 1
(b) Let 1 E₁ = -2 - 0 0 0 1 0 01 E₂ = 1 0 -3 Compute Y = E3E2E1 and its inverse Y-1. Compute Z = E1 E2 E3 and its inverse Z-¹. 00 10 0 1 E3 = 1 0 0 0 1 0 0-4 1
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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Question
I'm really struggling with part b. Multiplying the matrices together is simple but I'm not great at using the Guass Jordan process to find the inverse of the matrix. Could you show each elementary row operation that you used to find the inverses of both matrix Y and Z?
![(a) Find LU- and LDU-decomposition of the matrix
1 0 1
A = 2 2 5
345
(b) Let
E₁
=
100]
-2 10
0
0 1
E2
=
1
0
-3
=
Compute Y E3E2E₁ and its inverse Y-1.
Compute Z= E₁ E2 E3 and its inverse Z-¹.
00
10
0 1
.
E3
=
[10
0
0
1
-4
0
1](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3414f6b8-acb6-4d57-a5de-a971cbe05261%2Fdc8078ac-e21b-4b9a-a377-828873e5e153%2Fkrc3em_processed.png&w=3840&q=75)
Transcribed Image Text:(a) Find LU- and LDU-decomposition of the matrix
1 0 1
A = 2 2 5
345
(b) Let
E₁
=
100]
-2 10
0
0 1
E2
=
1
0
-3
=
Compute Y E3E2E₁ and its inverse Y-1.
Compute Z= E₁ E2 E3 and its inverse Z-¹.
00
10
0 1
.
E3
=
[10
0
0
1
-4
0
1
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