1. Eigenvectors of a symmetric matrix are orthogonal, but only for distinct eigenvalues

2. The Trapezoidal rule is a numerical method that approximates the value of a.______________.

3. 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

4. Power method is applicable if the eigen vectors corresponding to eigen values are linearly independent.

5. Central difference method seems to be giving a better approximation, however it requires more computations.

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

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

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

9. If x is an eigen value corresponding to eigen value of V of a matrix A. If a is any constant, then x – a is an eigen value corresponding to eigen vector V is an of the matrix A - a I.

10. Iterative algorithms can be more rapid than direct methods

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

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

13. If the root of the given equation lies between a and b, then the first approximation to the root of the equation by bisection method is ……

14. Sparse matrix is a matrix with ……….

15. While solving a system of linear equations, which of the following approach is economical for the computer memory?

16. Differences methods find the ________ solution of the system.

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

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

19. The determinant of a _______ matrix is the product of the diagonal elements

20. An improper integral is the limit of a definite integral as an endpoint of the interval of integration approaches either a specified real number or ∞ or -∞ or, in some cases as both endpoints approach limits.

21. The Gauss-Seidel method is applicable to strictly diagonally dominant or symmetric positive definite matrices A.

22. Below are all the finite difference methods EXCEPT _________.

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

24. Power method is applicable if the eigen values are ______________.

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

26. An indefinite integral may _________ in the sense that the limit defining it may not exist

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

28. Sparse matrices arise in computing the numerical solution of …………….

29. Generally, Adams methods are superior if output at many points is needed

30. Simpson’s rule is a numerical method that approximates the value of a definite integral by using polynomials