MTH603 Grand Quiz Fall 2020 by Instructor Munir

MTH603 Numerical Analysis · Grand Quiz Fall 2020 · Department of MCS · Compose By · MUNIR HUSSAIN & · ASAD MUNIR · Semester 3rd · OBJECTIVE

Q1. Two matrices with the same characteristics polynomial need not be similar.

1. True
2. False

Correct answer: True

Q2. If A =[323] then by using (Gaussian Elimination Method) the value of A-1 will be:

1. none
2. [1/2 0 0 -2 -3/2 -½
3. None

Correct answer: [1/2 0 0 -2 -3/2 -½

Q3. The characteristics polynomial of 3 x 3 identity matrix is ____. If x is the eigen values of the given 3x3 identity matrix. Where symbol ^ shiw power.

1. (x-1)^3
2. (x+1)^3
3. (X+3)^1
4. None

Correct answer: (x-1)^3

Q4. If the Relaxation method is applied on the system: 2x+3y=1, 3x+2y=-4, then largest residual in !st iteration will reduce to __

1. Zero
2. 4
3. 3
4. 2

Correct answer: Zero

Q5. Relaxation Method is a/an____

1. Direct method
2. Iterative method

Correct answer: Iterative method

Q6. Direct method can be more rapid than iterative aglorithms.

1. True
2. False

Correct answer: True

Q7. Let [A] be a 3x3 real symmetric matrix with |a23| be numerically the largest off-diagonal element of A, then we can construct orthogonal matrix S1 by Jacobi method

1. [ cos thetha –sin 0]
2. [ 1 0 0 0 cos –sin] \\ not conform

Correct answer: [ 1 0 0 0 cos –sin] \\ not conform

Q8. While using Relaxation method, rhich of the following is the Residuals for 1st iteration on the system, 2x+3y=1, 3x+2y=4 ?

1. (2,3)
2. (3,-2)
3. (1,4)
4. (-2,3)

Correct answer: (1,4)

Q9. While using the system: x-2y=1, x+4y=4 by Gauss-Seidel method. Which of the following ordering is feasible to have good approximate solution?

1. X+4y=1, x-2y=4
2. X+2y=1, x-4y=4
3. No need to recorder
4. X+4y=4

Correct answer: No need to recorder

Q10. 3x4 – 2x2 -24=0 has at least ___ real root(s)?

1. 1
2. 2
3. 3
4. 4

Correct answer: 2

Q11. An eigenvector V is said to be normalized if the coordinate of the largest magnitude is equal to zero.

1. True
2. False

Correct answer: False

Q12. If nxn matrices A and B are similar, then they have the ___ eigenvalues (with the same multiplicities).

1. Same
2. Different

Correct answer: Same

Q13. In Jacobi’s Method, the rate of convergence is quite slow compared

1. True
2. False

Correct answer: True

Q14. While using Relaxation method, which of the following is the largest Residual for 1st iteration on the system: 2x+3y=1, 3x+3y=-4?

1. -4
2. 3
3. -3
4. 4

Correct answer: -4

Q15. In Jacobi’s method after finding D1, the sum of the diagonal elements of D1 should be ____ to the sum of the diagonal elements of the original matrix A.

1. Greater than
2. Less than
3. Same
4. Different

Correct answer: Same

Q16. If the determinant of a matrix A is equal to zero then the stsyem of equations will have___

1. Unique solution
2. On solution
3. Infinitely many solution
4. On solution or Infinitely many solution

Correct answer: On solution or Infinitely many solution

17. In the context of Jacobi’s method for finding Eigen values and Eigen

diagonal values of Orthogonal Matrix?

1. Cos(theta), -Cos(theta)
2. Sin(theta), Cos(theta)
3. Sin(theta), -Sin(theta)
4. –Sin(theta), Cos(theta)

Correct answer: Sin(theta), -Sin(theta)

18. The Gaussian elimination method fails if any of the pivot elements becomes___