This practice GATE test includes only linear algebra questions which are part of the GATE mathematics question paper. Solve GATE practice tests to get high GATE score in GATE 2012 exam.

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Determinant of the matrix is ….......

-24

0

11

-48

Eigen vector(s) of the matrix ,’k’ is not equal to 0 is(are).........

(0,k,0)

(0,0,1)

(0,0,k)

(k,0,0)

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

A =

AB = BA

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 ?

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.

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

det(kA) = det(A)

det(AB) = det(A)det(B)

det(A+B) = det(A)+det(B)

det() = 1/det()

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

3

1

2

5

If , where A is a real matrix, then A is …

orthogonal

symmetric

normal

hermitian

Nullity of the matrix A= is…

4

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 ?

S1 is true,S2 is false

S1 and S2 are both true

S1 is false,S2 is true

S1 and S2 are both false

The rank of the matrix is …....

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

row is the same as the second row of A

row is all zero

column is the same as the second column of A

row is the same as its second row

Rank of the matrix is…....

Rank of the matrix is …....

The system of equations, 2x+4y=10, 5x+10y=25

has only two solutions

has infinite solutions

has only one solution

has no unique solution

if A=, then .....

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