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1. The matrix

0 6 66 0 6

6 6 0

is a matrix

(a) Orthogonal

(b) Skew-symmetric

(c) Nilpotent

(d) Symmetric

2. If A = 2 1

0 1

and B = 1 2

1 0

then (A + B)

T

=

(a)

3 1

1 3

(b)

3 3

1 1

(c)

3 1

3 1

(d)

1 3

3 1

3. Find the value of x such that A is singular were A =

3 x 2 22 4 x 12 4 (1 + x)

(a) 4

(b) 3

(c) 5

(d) 2

If A =

1 0 0 1 1 1

and B =

1 0 02 1 03 4 1

4. (a) A is row equivalent to B only when =0, = 3 and = 0

(b) A is row equivalent to B only when =2, = 3 and = 0

(c) A is row equivalent to B only when =2, = 0 and = 4

(d) A is row equivalent to B only when =2, = 3 and = 4

5. If A =

3 2

5 6

and B =

1 3

2 5

are such that 2A + 3B + X =0 , then X =

(a)

9 1316 27

(b) 9 1316 27(c)

9 1316 27

(d)

9 1316 27

6. The rank of a 3 5 matrix in which one row is a constant multiple of the other is lessthan or equal to(a) 1

(b) 3

(c) 5

(d) 2

7. The rank of a unit (identity) matrix of order 4 is

(a) 3

(b) 1

(c) 4

(d) 2

8. The rank of a matrix A =

1 2 3

0 x 4

1 1 1

is 2, then the value of x is

(a) 3

(b) 6

(c) 4

(d) 5

9. The necessary and sufficient condition that the system of equations AX = B is consistent if

(a) R(AB) > R(A)

(b) R(AB) < R(A)

(c) R(AB) = R(A)

(d) R(AB) = R(A)

10. If L =

1 2 30 1 4

0 0 1

and X =

xy

z

then the system L X = 0 has a solution

(a) x = -1, y = 1, z = 1

(b) x = 0, y = 0, z = 0

(c) x = 1, y = 1, z = 0

(d) x = 1, y = 1, z = 1

11. If A =

2 00 1

then the characteristic equation of A2 is

(a) 2 5 + 24 = 0(b) 2 + 6 + 4 = 0

(c) 2 + 5 - 4 = 0

(d) 2 5 + 4 = 0

12. Eigen values of A =

1 03 2

are

(a) - 1, -2

(b) 1,2

(c) 0,1

(d) 2,313. If one of the eigen value is zero, then |A| is

(a) non - zero

(b) zero

(c) - |A |(d) unity

14. The normalized form of eigen vector for

21

1

is

(a) 1/6 21

1

(b) 1/

6

21

1

(c) 1/

6

21

1

(d) 1/

6

2

11

15. If X is an eigen vector of A corresponding to an eigen value and k is any non zero scalar, then is an eigen

vector of A for the same eigen value .

(a) kX

(b) -kX

(c) - X

(d) X

16. Every square matrix satisfies its equation

(a) Non linear

(b) Linear(c) characteristic

(d) quadratic

17. The characteristic equation of the square matrix A =

2 51 3

is 2 + - 11 = 0 , then A2 is

(a)

9 51 14

(b)

9 51 14

(c) 9 5

10 3

(d)

9 51 14

18. The diagonal matrix has the eigen values of A as its elements

(a) diagonal

(b) real

(c) row

(d) positive

19. If1 , 2 , 3 are the eigen values of matrix A and An = BDnB1 then Dn =

(a)

n

10 0

0 n2

00 0 n

3

(b)

n

10 0

0 n2

00 0 n

3

(c)

1 0 00

20

0 0 3

(d)

n1

0 00 n

20

0 0 n

3

20. If X1 =

13

, X2 =

21

are the eigen vectors of A, then the normalized modal matrix of A is

(a)

110

25

310

15

(b)

110

25

310

15

(c)

110

25

310

15

(d) 1

10

25

310

15

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