MTH603Numerical 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, 6x2x+3x=1, x+x5x=13
 2x+7x+2x=5, 6x2x+3x=1, x+x5x=13
 x+x5x=13, 6x2x+3x=1, 2x+7x+2x=5
 6x2x+3x=1, 2x+7x+2x=5, x+x5x=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 offdiagonal then which of the following will be its corresponding offdiagonal 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 nonzero 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+5x3x=12, 2x4x+7x=15
 9x+5x3x=12, x+12x+5x=8, 2x4x+7x=15
 2x4x+7x=15, x+12x+5x=8, 9x+5x3x=12
 9x+5x3x=12, 2x4x+7x=15, x+12x+5x=8
10. Let[A] be a 3 x 3 real symmetric matrix with a be numerically the largest offdiagonal 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 ith 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 = 2a_{13}/a_{11}a_{33} ✔
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

S_{1} = [ 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 GaussSeidel 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

S_{1} = [ 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 GaussJacobi’s method, the corresponding elements of x_{i}^{(r+1)} replaces those of x_{i}^{r} 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?
6x_{1} – 2x_{2} + 3x_{3} = 1
2x_{1} + 7x_{2} + 2x_{3} = 5
x_{1} + x_{2} – 5x_{3} = 13
 dx_{3} = R_{3}/a_{33} ✔
31. Let A be a 3 x 3 real symmetric matrix with a_{23} be the numerically largest offdiagonal element then using Jacobi’s method the value of theta can be found by
 tan 2 Θ = 2a_{23}/a_{22}a_{33 }✔
32. The linear equation; 0x+0y=2 has ___ solution/solutions
 unique
 no solution ✔
 infinite many
 finite many
33. The root of the equation xe^{x}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 Δ^{2}y 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
 GaussSeidel
 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 Δ^{2}y 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 GaussSeidel 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. GaussJordan method is similar to ___
GaussSeidel 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.