1- Find the inverse by Gauss Elimination method: 01 2 1 [1 2 3] ii- A = 4 5 6 iii- A =-2 2 l7 8 9] 2 i- A = |-2 1 5 -4 1l 1 2 -21
1- Find the inverse by Gauss Elimination method: 01 2 1 [1 2 3] ii- A = 4 5 6 iii- A =-2 2 l7 8 9] 2 i- A = |-2 1 5 -4 1l 1 2 -21
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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![Chapter Three: Mairix Analysis
Dr. Fadhil Sahib Al-Moussawi
Tutorial Sheet No. 3
Matrix Analysis
1- Find the inverse by Gauss Elimination method:
0 01
[1 2 3]
ii- A = 4 5 6 iii- A =|-2 2
l7 8 9l
2
1
2
i-
A = -2 1 0
1
-4 1
2- Use Gauss Elimination method to solve the following system:
2 -2
4x1 + 5x2 + X3 = 2
3x1 + 2x2 - x3 = 4
i- 2x1 - x2 +2x3 10
X1 - 3x2 - 4x3 = 5.
ii-
X1 - 2x2 - 3x =7
3x1 - x2- 2x3 = 1.
3- Find Eigenvalues and Eigenvectors for the following matrices:
[1 0 4
[5 -6
1
i- A = " ii- A = 0 2 0i- A = 1 1
[3 10]
l3 1 -3]
4- Determine the rank of the following matrices:
L3
1.
[3 4 5]
i-A = 4 7 6 ii- A= 1 2 3 i- A = 1 5 6
4 5 6
5- Determine whether cach of the following is singular or nonsingular:
[1 2 8]
[3 9
21
l9 5 3]
l2 7 4]
[3 2 41
i- A = 1 7 3 ii- A = 5 1 6 ii - A=4 7 6
Iz o 3]
[4 1
-2]
[1 2 8]
l5 8 1
9 5 3
6- Check if each of the following is orthogonal or not:
1-A= 4- A =
iit - A = I
7- Solve the following circuit using Gauss Elimination method, V/R=1;
R
R](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F65efc8b9-1385-438e-b9e2-72bacc09d87a%2Fecdc7d9e-391f-4867-b32f-f8b702b301d7%2Fcptwgbo_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Chapter Three: Mairix Analysis
Dr. Fadhil Sahib Al-Moussawi
Tutorial Sheet No. 3
Matrix Analysis
1- Find the inverse by Gauss Elimination method:
0 01
[1 2 3]
ii- A = 4 5 6 iii- A =|-2 2
l7 8 9l
2
1
2
i-
A = -2 1 0
1
-4 1
2- Use Gauss Elimination method to solve the following system:
2 -2
4x1 + 5x2 + X3 = 2
3x1 + 2x2 - x3 = 4
i- 2x1 - x2 +2x3 10
X1 - 3x2 - 4x3 = 5.
ii-
X1 - 2x2 - 3x =7
3x1 - x2- 2x3 = 1.
3- Find Eigenvalues and Eigenvectors for the following matrices:
[1 0 4
[5 -6
1
i- A = " ii- A = 0 2 0i- A = 1 1
[3 10]
l3 1 -3]
4- Determine the rank of the following matrices:
L3
1.
[3 4 5]
i-A = 4 7 6 ii- A= 1 2 3 i- A = 1 5 6
4 5 6
5- Determine whether cach of the following is singular or nonsingular:
[1 2 8]
[3 9
21
l9 5 3]
l2 7 4]
[3 2 41
i- A = 1 7 3 ii- A = 5 1 6 ii - A=4 7 6
Iz o 3]
[4 1
-2]
[1 2 8]
l5 8 1
9 5 3
6- Check if each of the following is orthogonal or not:
1-A= 4- A =
iit - A = I
7- Solve the following circuit using Gauss Elimination method, V/R=1;
R
R
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