GATE Question Papers Mathematics for GATE 2011 Exam Preparation

Question

Determinant of the matrix $\dbinom{6 -8 1 1}{0 2 4 6}{0 0 4 8}{0 0 0 -1}$ is ….......

Possible Answers

Selected	Possible Answer
	-24
	0
	11
	-48

Question

Eigen vector(s) of the matrix $\dbinom{0 0 k}{0 0 0}{0 0 0}$ ,’k’ is not equal to 0 is(are).........

Possible Answers

Selected	Possible Answer
	(0,k,0)
	(0,0,1)
	(0,0,k)
	(k,0,0)

Question

If A and B be real symmetric matrices of size nXn, then….....

Possible Answers

Selected	Possible Answer
	A =
	AB = BA
	= BA
	= 1

Question

let Ax=B be a system of linear equations, where ‘A’ is an mXn matrix and ‘B’ is a mX1 column vector and ‘x’ is a nX1 column vector of unknown, which of the following is FALSE ?

Possible Answers

Selected	Possible Answer
	the system has a solution if and only if, both A and the aumented matrix[AB] have the same rank.
	if m
	if m=n and B is a non zero vector, then the system has a unique solution.
	the system will have only a trivial solution when m=n, B is zero vector and rank(A)=n.

Question

If A and B are same matrices of size nXn, then which of the following statement is not true ?

Possible Answers

Selected	Possible Answer
	det(kA) = det(A)
	det(AB) = det(A)det(B)
	det(A+B) = det(A)+det(B)
	det() = 1/det()

Question

For which value of K, the following system is consistant ? 2x-5Ky+6z=0, Kx+2y-2z=0, 2x+2y-Kz=0

Possible Answers

Selected	Possible Answer
	3
	1
	2
	5

Question

If A^T = A^-1 , where A is a real matrix, then A is …

Possible Answers

Selected	Possible Answer
	orthogonal
	symmetric
	normal
	hermitian

Question

Nullity of the matrix A= $\dbinom{-1 4 2}{1 3 2}{-2 1 0}{2 6 4}$ is…

Possible Answers

Selected	Possible Answer
	4
	1
	2
	3

Question

consider the following statements …. S1: sum of the two singular nXn matrices may be non-singular. S2: sum of two non-singular nXn matrices may be singular. which of the following statement is correct ?

Possible Answers

Selected	Possible Answer
	S1 is true,S2 is false
	S1 and S2 are both true
	S1 is false,S2 is true
	S1 and S2 are both false

Question

The rank of the matrix $\dbinom{0 0 -3}{9 3 5}{3 1 1}$ is …....

Possible Answers

Selected	Possible Answer
	2
	1
	0
	3

Question

let A= (a_ij) be an n-rowed square matrix and I_12 be the matrix obtained by interchanging the first and second rows of the n-rowed Identity matrix, then AI_12 is such that its first…..

Possible Answers