1- Find the inverse by Gauss Elimination method: [1 2 3] ii- A = 4 5 6 l7 8 9/ 1 01 1 iii- A =-2 2 2 -2 2 i- A =|-2 1 1 -4 1 1
1- Find the inverse by Gauss Elimination method: [1 2 3] ii- A = 4 5 6 l7 8 9/ 1 01 1 iii- A =-2 2 2 -2 2 i- A =|-2 1 1 -4 1 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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![1- Find the inverse by Gauss Elimination method:
01
[1 2 3]
ii- A = 4 5 6 iii- A =-2 2
l7 8 99
1
[ 2
1
i-
A =-2
1
5
-4 1]
2
-21
2- Use Gauss Elimination method to solve the following system:
4x1 +5x2 + x3 = 2
3x1 + 2x2 - x3 4
i- 2x1 - x2+ 2x3 = 10
X1 - 3x2 - 4x3 = 5.
ii-
X1 - 2x2 - 3x3 =7
X2 - 2x3 1.
3x1
3- Find Eigenvalues and Eigenvectors for the following matrices:
[1 0 4
ii- A = 0 2 0
l3 1 -3]
[5 -6 1
[3 10]
l2
iii- A = 1
13
i-
1
1
4- Determine the rank of the following matrices:
[1 2 8]
i- A = 4 7 6 ii- A= 1 2 3
9 5 3]
[3 4 51
[3 9 2]
iii- A = 1 5 6
l2 7 4)
14 5 6
5- Determine whether each of the following is singular or nonsingular:
[1 2 81
iii - A =4 7 6
9 5 3]
[4 1 -21
[3 2 41
ii - A = 5 1 6
l2 0 3]
i- A=1 7
3
l5 8
1
6- Check if each of the following is orthogonal or not:
il - A=:
ii - A
1 [1 11
lo -1
i- A =
7- Solve the following circuit using Gauss Elimination method, V/R=1;
R
R
R
R
12](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1d7c5fed-151e-4ada-b364-c552ac3b1bd1%2Ffffca0fa-c2a3-417e-b5c2-855792e59b05%2F066ugdh_processed.jpeg&w=3840&q=75)
Transcribed Image Text:1- Find the inverse by Gauss Elimination method:
01
[1 2 3]
ii- A = 4 5 6 iii- A =-2 2
l7 8 99
1
[ 2
1
i-
A =-2
1
5
-4 1]
2
-21
2- Use Gauss Elimination method to solve the following system:
4x1 +5x2 + x3 = 2
3x1 + 2x2 - x3 4
i- 2x1 - x2+ 2x3 = 10
X1 - 3x2 - 4x3 = 5.
ii-
X1 - 2x2 - 3x3 =7
X2 - 2x3 1.
3x1
3- Find Eigenvalues and Eigenvectors for the following matrices:
[1 0 4
ii- A = 0 2 0
l3 1 -3]
[5 -6 1
[3 10]
l2
iii- A = 1
13
i-
1
1
4- Determine the rank of the following matrices:
[1 2 8]
i- A = 4 7 6 ii- A= 1 2 3
9 5 3]
[3 4 51
[3 9 2]
iii- A = 1 5 6
l2 7 4)
14 5 6
5- Determine whether each of the following is singular or nonsingular:
[1 2 81
iii - A =4 7 6
9 5 3]
[4 1 -21
[3 2 41
ii - A = 5 1 6
l2 0 3]
i- A=1 7
3
l5 8
1
6- Check if each of the following is orthogonal or not:
il - A=:
ii - A
1 [1 11
lo -1
i- A =
7- Solve the following circuit using Gauss Elimination method, V/R=1;
R
R
R
R
12
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