Use the Gauss-Jordan method to find the inverse of the following matrix: 2 10 1 1 5 0 [ 3 14 4 To this end, create the augmented matrix [A|1] and use elementary row operations to reduce it to [I|A-1] 1 0 0 5 0 0 1 0 2 10 1 1 5 0 0 1 0 2 10 1 1 0 0 3 14 4 0 0 1 3 14 4 0 0 1 5 0 1 0 R2- 0 1 3 14 4 0 1 1. 5 0 1 0 R3- 1. 0 1 1 0 -1 4 -3 1 1. 5 0 1 0 0 -1 4 0 1 1. -2 0 1 5 -R2 0 1 -4 -1 0 0 1. -2

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter9: Systems Of Equations And Inequalities
Section9.7: The Inverse Of A Matrix
Problem 30E
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Question
15 0
1
R2+
R3
0 1 0
4
-1
0 0 1
1
-2
1 00
R-5 R2
0 1 0
4
-5
-1
0 0 1
1
-2
You have now transformed the augmented matrix [A|I] into [I|A]. Copy the inverse A
here:
A-1
4
-5
-1
-2
Use A-1 to find the solution of the system Ay
||
N
Transcribed Image Text:15 0 1 R2+ R3 0 1 0 4 -1 0 0 1 1 -2 1 00 R-5 R2 0 1 0 4 -5 -1 0 0 1 1 -2 You have now transformed the augmented matrix [A|I] into [I|A]. Copy the inverse A here: A-1 4 -5 -1 -2 Use A-1 to find the solution of the system Ay || N
Use the Gauss-Jordan method to find the inverse of the following matrix:
2 10 1
5 0
3 14 4
To this end, create the augmented matrix [A|1] and use elementary row operations to reduce it to [I|A-1]:
2 10 1
1 00
1
5 0
0 1 0
0 1 0
R R2
1 0 0
1
5 0
2 10 1
3 14 4
0 0 1
3 14 4
0 0 1
5 0
1 0
R2-
|R1
0 1
3 14 4
0 1
1
5 0
1 0
R3-
R.
0 1
1
0 -1 4
-3 1
5 0
1 0
0 -1 4
1
0 1
1
-2 0
15
1
-R2
0 1 -4
-1
0 0
1.
1
-2
Transcribed Image Text:Use the Gauss-Jordan method to find the inverse of the following matrix: 2 10 1 5 0 3 14 4 To this end, create the augmented matrix [A|1] and use elementary row operations to reduce it to [I|A-1]: 2 10 1 1 00 1 5 0 0 1 0 0 1 0 R R2 1 0 0 1 5 0 2 10 1 3 14 4 0 0 1 3 14 4 0 0 1 5 0 1 0 R2- |R1 0 1 3 14 4 0 1 1 5 0 1 0 R3- R. 0 1 1 0 -1 4 -3 1 5 0 1 0 0 -1 4 1 0 1 1 -2 0 15 1 -R2 0 1 -4 -1 0 0 1. 1 -2
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