## Sunday, 27 December 2020

### MTH603-Numerical Analysis Quiz MCQs Lecture 1-22 Midterm Objective Questions | SUPERSTARWEBTECH

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) ✔