Find the inverse of the following matrix 2 3 0 1 4 6 ol
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
![Find the inverse of the following matrix
1
2 3
0
1 4
15
6 ol
use this format: (show what is done to the rows)
(A|In).
Let us see an example. Suppose that
1
2 -3
A =
2
5 -8
-3 -5 8
First we make the super
augmented matrix
1
1 0
0
2 -3
-8
2
5
0 1 0
-3 -5 8
0 01/
Now apply Gaussian elimination. Multiply the first row by -2 and
3 and add them to the second and third row.
1 0 0
1 2 -3 |
0 1 -2
-2 10
0 1 -1 |
3 01
Now multiply the second row by -1 and add it to the third row to get
1 2 -3 1
0 1 -2
0 0 1
1 0
-2 1 0
5 -1 1,
This completes the Gaussian elimination. Now we continue Gauss Jor-
dan elimination Multiply the third row by 2 and 3 and add it to the
second and first row, to get
1 2 0 16 -3 3
0108 -1 2
0 0 1 5 -1 1,
The last step is to multiply the second row by -2 and add it to the
first row,
1000-1
0108-1 2
0015-1
The inverse matrix is
B 8
=
-1 2
5 -1
One can check that indeed AB = BA = 13.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4c061177-af18-4375-acf2-4edd9910e36e%2F4327bf8f-d202-4271-95d7-242a710fa699%2Fmp7ue8c_processed.png&w=3840&q=75)
Transcribed Image Text:Find the inverse of the following matrix
1
2 3
0
1 4
15
6 ol
use this format: (show what is done to the rows)
(A|In).
Let us see an example. Suppose that
1
2 -3
A =
2
5 -8
-3 -5 8
First we make the super
augmented matrix
1
1 0
0
2 -3
-8
2
5
0 1 0
-3 -5 8
0 01/
Now apply Gaussian elimination. Multiply the first row by -2 and
3 and add them to the second and third row.
1 0 0
1 2 -3 |
0 1 -2
-2 10
0 1 -1 |
3 01
Now multiply the second row by -1 and add it to the third row to get
1 2 -3 1
0 1 -2
0 0 1
1 0
-2 1 0
5 -1 1,
This completes the Gaussian elimination. Now we continue Gauss Jor-
dan elimination Multiply the third row by 2 and 3 and add it to the
second and first row, to get
1 2 0 16 -3 3
0108 -1 2
0 0 1 5 -1 1,
The last step is to multiply the second row by -2 and add it to the
first row,
1000-1
0108-1 2
0015-1
The inverse matrix is
B 8
=
-1 2
5 -1
One can check that indeed AB = BA = 13.
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