MTH603-Numerical Analysis Quiz MCQS #Objective #Questions #MidTerm
1. If n x n matrices A and B are similar, then they have the ___ eigenvalues (with the same multiplicities)
- same ✔
- different
2. If the product of two matrices is an identity matrices that is AB = I, then which of the following is true?
- A is transpose of B
- A is inverse of B ✔
- A is singular
- B is singular
3. Iterative algorithms can be more rapid than direct methods.
- False
- True ✔
4. While using Relaxation method, which of the following is the largest Residual for 1st iteration on the system; 2x + 3y = 1, 3x + 2y = -4?
- -4 ✔
- 3
- 2
- 1
5. Which of the following systems of linear equations has a strictly diagonally dominant coefficient matrix?
- -2x+7x+2x=5, 6x-2x+3x=1, x+x-5x=-13
- -2x+7x+2x=5, 6x-2x+3x=1, x+x-5x=-13
- x+x-5x=-13, 6x-2x+3x=1, -2x+7x+2x=5
- 6x-2x+3x=1, -2x+7x+2x=5, x+x-5x=-13
6. In the context of Jacobi’s method for finding Eigen values and Eigen vectors of a real symmetric matrix of order 2*2, if |-5| be its largest off-diagonal then which of the following will be its corresponding off-diagonal values of Orthogonal Matrix?
- Cos(theta), -Cos(theta)
- Sin(theta), Cos(theta)
- Sin(theta), -Sin(theta)
- -Sin(theta), Cos(theta)
7. While using power method, from the resultant normalize vector
8. Every non-zero vector x is an eigenvector of the identity matrix with Eigen value___
- one
- two
- three
- four
9. Which of the following systems of linear equations has a strictly diagonally coefficient matrix?
- -x+12x+5x=8, 9x+5x-3x=12, 2x-4x+7x=-15
- 9x+5x-3x=12, -x+12x+5x=8, 2x-4x+7x=-15
- 2x-4x+7x=-15, -x+12x+5x=8, 9x+5x-3x=12
- 9x+5x-3x=12, 2x-4x+7x=-15, -x+12x+5x=8
10. Let[A] be a 3 x 3 real symmetric matrix with |a| be numerically the largest off-diagonal element of A, then we can construct orthogonal matrix S1 by Jacobi’s method as
11. If the pivot element happens to be zero, then the i-th column elements are searched for the numerically ___ element
- Smallest
- Largest ✔
12. Exact solution of 2/3 is not exists
- True ✔
- False
13. A and its transpose matrix have ___ eigenvalues
- same ✔
- different
14. If n x n matrices A and B are similar, then they have the different eigenvalues (with the same multiplicities)
- True ✔
- False
15. Power method is applicable if the eigen values are real and distinct
- True ✔
- False
16. By using determinants, we can easily check that the solution of the given system of linear equation ___ and it is ___
- exists, unique ✔
- exists, consistent
- trivial, unique
- nontrivial, inconsistent
17. Power method is applicable if the eigen vectors corresponding to eigen values are linearly ___
- independent ✔
- dependent
18. When the condition of diagonal dominance becomes true in Jacobi’s Method. Then its means that the method is ___
- Stable
- Unstable
- Convergent ✔
- Divergent
19. While using Jacobi method for the matrix
| A = [ | 1 | 1/4 | 1/3 | ] |
| 1/4 | 1/3 | 1/2 | ||
| 1/3 | 1/2 | 1/5 |
the value of ‘theta Θ’ can be found as
- tan 2Θ = 2a13/a11-a33 ✔
20. While using Jacobi method for the matrix
| A = [ | 1 | 1/4 | 1/2 | ] |
| 1/4 | 1/3 | 1/4 | ||
| 1/2 | 1/4 | 1/5 |
and ‘theta Θ=0.4480’ the orthogonal matrix S1 will be given by
-
S1 = [ cos 0.4480 0 -sin 0.4480 ] ✔ 0 1 0 sin 0.4480 0 cos 0.4480
21. Full pivoting, in fact, is more ___ than the partial pivoting
- Easiest
- Complicated ✔
22. While using the Gauss-Seidel Method for finding the solution of the system of equation, the following system
x + 2y + 2z = 3
x + 3y + 3z = 2
x + y + 5z = 2
- x = 3 – 2y – 2z, y = 2/3 – x/3 – z, z = 2/5 – x/5 – y/5
23. By using determinants, we can easily check that the solution of the given system of linear equation exists and it is unique
- True ✔
- False
24. While using Jacobi method for the matrix
| A = [ | 1 | 1/4 | 1/3 | ] |
| 1/4 | 1/3 | 1/2 | ||
| 1/3 | 1/2 | 1/5 |
and ‘theta Θ= 0.7191’ the orthogonal matrix S1 will be given by
-
S1 = [ cos 0.7191 0 -sin 0.7191 ] ✔ 0 1 0 sin 0.7191 0 cos 0.7191
25. The linear equation x + y = 1 has ___ solution/solutions
- no solution
- unique ✔
- infinite many
- finite many
26. For a system of linear equations, the corresponding coefficient matrix has the value of determinant; |A|=-3, then which of the following is true?
- The system has unique solution ✔
- The system has finite multiple solutions
- The system has infinite many solutions
- The system has no solution
27. In Gauss-Jacobi’s method, the corresponding elements of xi(r+1) replaces those of xir as soon as they become available
- True
- False ✔
28. An augmented matrix may also be used to find the inverse of a matrix by combining it with the ___ matrix
- Inverse
- Square
- Identity ✔
- None
29. Power method is applicable it the eigen vectors corresponding to eigen values are linearly independent
- True ✔
- False
30. While using the relaxation method for finding the solution of the below given system, which of the following increment will be introduced?
6x1 – 2x2 + 3x3 = 1
-2x1 + 7x2 + 2x3 = 5
x1 + x2 – 5x3 = -13
- dx3 = R3/a33 ✔
31. Let |A| be a 3 x 3 real symmetric matrix with |a23| be the numerically largest off-diagonal element then using Jacobi’s method the value of theta can be found by
- tan 2 Θ = 2a23/a22-a33 ✔
32. The linear equation; 0x+0y=2 has ___ solution/solutions
- unique
- no solution ✔
- infinite many
- finite many
33. The root of the equation xex-5=0 is bounded in the interval
- [-2, 1]
- [-1, 1]
- [0, 1] ✔
- [1, 2]
34. Which of the following is a forward difference table for the given values of x and y?
x 0.1 0.5 0.9
y 0.003 0.148 0.370
-
x y Δy Δ2y 0.1 0.003 0.145 0.077 0.5 0.148 0.222 ✔ 0.9 0.37
35. In ___ method, a system is reduced to an equivalent diagonal form using elementary transformations
- Jacobi’s
- Gauss-Seidel
- Relaxation
- Gaussian elimination ✔
36. If the determinant of a matrix A is not equal to zero then the system of equations will have ___
- a unique solution ✔
- many solutions
- infinite many solutions
- None
37. A 3 x 3 identity matrix have three and ___ eigen values
- same ✔
- different
38. Numerical methods for finding the solution of the system of equations are classified as direct and ___ methods
- Indirect
- Iterative ✔
- Jacobi
- None
39. Which of the following is a forward difference table for the given values of x and y?
x 0.1 0.7 1.3
y 0.003 0.248 0.697
-
x y Δy Δ2y 0.1 0.003 0.245 0.204 0.7 0.248 0.449 ✔ 1.3 0.697
40. While using Relaxation method, which of the following is the Residuals for 1st iteration on the system; 2x + 3y = 1, 3x + 2y = 4?
- (2, 3)
- (3, -2)
- (-2, 3)
- (1, 4) ✔
41. While solving by Gauss-Seidel method, which of the following is the first iterative solution for the system;
x – 2y = 1
x + 4y = 4?
(1, 0.75)
(0, 0)
(1, 0)
(0, 1)
42. Gauss-Jordan method is similar to ___
Gauss-Seidel method
Iteration’s method
Relaxation method
Gaussian elimination method
43. While using power method, the computed vector ####5
will be in normalized form as
44. In Jacobi’s method, the rate of convergence is quite ___ compared with other methods
slow
fast
45. While using power method, the computed vector ###7
will be in normalized form as
46. While using Gaussian Elimination method, the following augmented matrix
will reduce in identity matrix by performing ###8
47. Which of the following system is diagonally dominant ###10
48.
