MTH501 Midterm Past Papers by Junaid

1. If the determinant of the matrix A

multiplying any row of A with an integer value 4, then which of the following is true for the matrix B?

2. Let V be a five-dimensional vector space, and let S be a subset of V which spans V. Then S
3. The Elementary Row operations:  R R R and  R R R are

performed on to get 1 2 -5 -4 1 -6

Answer 1 2 -5

4. Let A and B be the square matrices. Then A and B are invertible with B A and A B if and only if AB AB equals to a (an) ________ matrix.

Identity

5. If λ is an eigenvector of A, then every nonzero vector x such that Ax = λx is called an ________ of A corresponding to ________.

Eigenvector, λ

6. If x + 2 is a factor of the characteristic polynomial of matrix C then an eigenvalue of C is

-2

7. Let A be n × n matrix, then A is invertible if and only if
8. Gauss-Seidel method is also termed as a method of
9. If one of the eigenvalues of is zero, n n

A

 it implies ___.

 is zero

10. If u + v = u + w, then:

v = w

11. If the determinant of the matrix A

adding 2 times of the second row in the first row of the matrix A, then which of the following is true for the matrix B?

12. Which of the following will be the Matrix Product corresponding to Linear

Combination: x y

x y

13. The solution of Ax = b exists if and only if b can be written as a linear

Columns

14. A sufficient condition for the jacobi's method to converge for the linear system Ax=b
15. Two simultaneous linear equations in two variables have no solution if their
16. Which of the following will be the Linear Combination corresponding to x y Answer x y
17. If a homogeneous system

Ax 

has a trivial solution, then which of the following is (are) the value(s) of the vector x?

18. A square matrix A is said to be diagonal if A is similar to a matrix

Diagonal matrix

Q19. Why inverse of the matrix A= [1 2] is NOT possible?

20. Which of the following Elementary Row operations would perform in order to

get 1 2 -5 -4 1 -6 ~ 0 9 -36 6 3 -4 0 -9 26 R R R R R R

Q21. What is the maximum possiblle number of pivots in a 6 × 6 matrix?

22. A homogeneous linear system always has the trivial solution: there are only two

The system has infinitely much solutionsnin addition to trivial solution

23. A system of linear equations is said to be homogeneous if the constant terms are all Zero
24. In A is a square matrix, then the minor of entry ith row and jth column is to be the determinant of the sub matrix that remains when the ith row and jth column of A are

Added

25. 7x is an algebraic term in which 7 is a ________ and x is a ________.