1. The Jacobi’s method is a method of solving a matrix equation on a matrix that has ____zeros along its main diagonal

2. The Gauss-Seidel method is applicable to strictly diagonally dominant or symmetric________ definite matrices A.

3. 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

4. The Jacobi iteration converges, if A is strictly diagonally dominant.

5. Eigenvalues of a symmetric matrix are all _______

6. A 3 x 3 identity matrix have three and __________eigen values

7. The eigenvectors of a square matrix are the non-zero vectors that, after being multiplied by the matrix, remain …………… to the original vector.

8. Sparse matrix is a matrix with ……….

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

10. Which of the following is equivalent form of the system of equations in matrix form; AX=B ?

11. Eigenvalues of a _________ matrix are all real

12. If n x n matrices A and B are similar, then they have the different eigenvalues (with the same multiplicities).

13. The determinant of a diagonal matrix is the product of the diagonal elements

14. How many Eigen vectors will exist corresponding to the function; Exp(ax) = e^ax, when the matrix operator is of differentiation?

15. Euler's Method numerically computes the approximate derivative of a function

16. 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?

17. In Jacobi’s Method, the rate of convergence is quite ______ compared with other methods

18. If we wanted to find the value of a definite integral with an infinite limit, we can instead replace the infinite limit with a variable, and then take the limit as this variable goes to _________.

19. The base of the decimal system is _______

20. If system of equations is inconsistent then its means that it has ………

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

22. While solving the system; x–2y = 1, x+4y = 4 by Gauss-Seidel method, which of the following ordering
is feasible to have good approximate solution?

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

24. In ……………… method, the elements above and below the diagonal are simultaneously made zero.

25. Numerical solution of 2/3 up to four decimal places is ________.

26. Bisection and false position methods are also known as bracketing method and are always

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

28. Jacobi’s Method is a/an………………

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

30. Let A be an n ×n matrix. The number x is an eigenvalue of A if there exists a non-zero vector v such that _______.