MTH603 Midterm Past Papers by Junaid

Q1. While solving a system of liner equation, which of the following approach is economical for the computer memory?

•  Direction
•  Graphical

2. The basic idea of relaxation method is to reduce the largest residual to

•  One
•  Two
•  Zero (page 83)

3. The Jacobi’s method is a method of solving a matrix equation on a matrix that has no zeros along its

•  Main diagonal (page 104)
•  Last column
•  Last row
•  First row

4. If A is a nxn triangular matrix (upper triangular, lower triangular) or diagonal matrix , the eigenvalues of A are the diagonal entries of A.

•  True
•  False

5. A 3 x 3 identity matrix have three and different Eigen values.

•  True
•  False

Q6. Which of the following is a reason due to which the LU decomposition of the system of linear equations; x+y = 1, x+y =2 is not possible?

•  Associated coefficient matrix is singular
•  All values of l’s and u’s can’t be evaluated
•  Determinant of coefficient matrix is zero
•  All are equivalent

7. Gauss - Jordan Method is similar to ……….

•  Relaxation Method
•  Gaussian elimination method (Page 95)

Q8. 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

8. Gauss–Seidel method is also known as method of …………….

•  Successive displacement (Page 263)
•  Iterations
•  False position

9. Jacobi’s Method is a/an………

•  Iterative method
•  Direct method

10. The characteristics polynomial of a 3x 3 identity matrix is __________, if x is the Eigen values of the given 3 x 3 identity matrix. Where symbol ^ shows power.

•  (X-1)^3
•  (x+1)^3
•  X^3-1
•  X^3+1

11. The can be used only to find the Eigen value of A that is largest in absolute value—we call this Eigen value the dominant Eigen value of A.

•  True
•  False

12. In …………… method, a system is reduced to an equivalent diagonal form using elementary transformations.

•  Jacobi’s
•  Gauss-Seidel
•  Relaxation
•  Gaussian elimination (Page 262)

13. The linear equation: 2x+0y-2=0 has -------- solution/solutions.

•  Unique (Page 48)
•  No solution
•  Infinite many
•  Finite many

14. Under elimination methods, we consider, Gaussian elimination and ……………methods.

•  Gauss-Seidel
•  Jacobi
•  Gauss-Jordan elimination (Page 48)

15. Which of the following method is not an iterative method?

•  Relaxation methods
•  Gauss-Jordan elimination method

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

•  True
•  False (page 97)

17. Exact solution of 2/3 is not exists.

•  True
•  False