Find the inverse of the matrix. 5 -1 4 1 135 1. A= 2. B= 244 1 - 11/
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
Advanced Math - Inverse of a Matrix
Solve the given equations by finding the inverse of a matrix. Example is in the second pic.
![Example
Find the inverse A
2R₁ + R₂
5R₁ + R3
Solution: We will use the augmented matrix to reduced row-echelon form.
2 0 1 1 0 0
1 0 1\2 12 00
-2 3 4 0 1 0
-2 3 4
0 1 0
-5 5 6 0 0 1
-5 5 6
0 0 1
R₂
R3
- R₂ + R3
30 R3
-R3 + R₁
-5/R3 + R₂
=
A-1
=
1 0 1\2 1\200
0 3 5 1 10
0 5 17\2 5 2 0 1
1\2 0 0
1 0
1\2
0 1 5 3
13 1\3 0
0 1 17 10 1\2 0 1\5,
201
-234
-556
1 0 1\2
0 1 5 3
0 0 1\30
0 0 1
R₁
1 0 1\2 1\2 00
0 1 5 3 13 13 0
1 0 0
-2 5 3
0 1 0
-8 17 - 10
0 0 1 5 10 6
Since the identity matrix I appears to the left we conclude the matrix to the right of the line is the inverse of A.
-25-3
-8 17
5 - 10
-
10
1\2 0 0
13 13 0
1\61\3 1\5,
5 10 6
-](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8a6e9848-9249-40a2-b72e-f57049e13d57%2Fe2dde3ae-5273-4d38-8875-55ef40dd46ee%2Fegtnkei_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Example
Find the inverse A
2R₁ + R₂
5R₁ + R3
Solution: We will use the augmented matrix to reduced row-echelon form.
2 0 1 1 0 0
1 0 1\2 12 00
-2 3 4 0 1 0
-2 3 4
0 1 0
-5 5 6 0 0 1
-5 5 6
0 0 1
R₂
R3
- R₂ + R3
30 R3
-R3 + R₁
-5/R3 + R₂
=
A-1
=
1 0 1\2 1\200
0 3 5 1 10
0 5 17\2 5 2 0 1
1\2 0 0
1 0
1\2
0 1 5 3
13 1\3 0
0 1 17 10 1\2 0 1\5,
201
-234
-556
1 0 1\2
0 1 5 3
0 0 1\30
0 0 1
R₁
1 0 1\2 1\2 00
0 1 5 3 13 13 0
1 0 0
-2 5 3
0 1 0
-8 17 - 10
0 0 1 5 10 6
Since the identity matrix I appears to the left we conclude the matrix to the right of the line is the inverse of A.
-25-3
-8 17
5 - 10
-
10
1\2 0 0
13 13 0
1\61\3 1\5,
5 10 6
-
![Find the inverse of the matrix.
5
- 1
4 1
1
1. A=
2. B=
3 5
244
1 - 11](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8a6e9848-9249-40a2-b72e-f57049e13d57%2Fe2dde3ae-5273-4d38-8875-55ef40dd46ee%2Firmgqke_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Find the inverse of the matrix.
5
- 1
4 1
1
1. A=
2. B=
3 5
244
1 - 11
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