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1. If A is a square matrix such that A2 = I then A is called

(a) unit matrix

(b) involutary

(c) symmetric

(d) nilpotent

2. If A =

1 a

0 1

what is An ? where n is positive integer.

(a)na 0

0 1

(b)

1 0

0 1

(c)

1 an

0 1

(d)

1 na

0 1

3. Matrix A is said to be skew - symmetric matrix ifAT =

(a) I

(b) -A

(c) A

(d) AT

4. If A =

0 1 2

1 0 3

2 3 0

, then A + AT =

(a) unit matrix

(b) symmetric matrix

(c) null matrix

(d) orthogonal matrix

5. The matrix A =

3 2 22 4 12 4 1

is

(a) Orthogonal matrix

(b) Unit matrix

(c) singular matrix

(d) non-singular matrix

6. If det A = 0, then A is said to be matrix.

(a) non singular matrix

(b) unit matrix

(c) singular matrix

(d) symmetric matrix

7. The inverse of an orthogonal matrix is

(a) singular

(b) diagonal

(c) Orthogonal

(d) symmetric

8. A matrix is multiplied with a non - singular matrix then the rank of the matrix is

(a) zero

(b) order of the matrix

(c) one

(d) remaining same

9. The system of equations x + y + 3z = 0, 4x + 3y + 8z = 0, 2x + y + 2z = 0 is

(a) no solution

(b) unique solution

(c) consistent

(d) In consistent

10. In the system AX = 0, if the number of equations is less than the number of unknowns then the system has

(a) no solution

(b) trivial solution

(c) zero solution

(d) non-trivial solution

11. If A =

8 42 2

then the characteristic equation of AT is

(a)2

+ 10

+ 24 = 0(b) 2 + 10 - 24 = 0

(c) 2 + 10 + 3 = 0

(d) 2 + 6 + 3 = 0

12. The sum of the eigen values of A =

0 1 20 0 5

2 4 0

is

(a) 0

(b) 2

(c) 1

(d) 3

13. The eigen vector corresponding to = 1 for the matrix

0 3 40 1 5

0 0 2

is

(a) ( 1, 1, 1 )

(b) ( k, 0, 0 )

(c) ( 0, k, 0 )

(d) (-k, 0, 0 )

14. If A and B one two non - singular matrics then the matrics AB and BA have the eigen values

(a) may or may not be the same

(b) of A

(c) different

(d) same

15. A and B are similar matrices and if X is an eigen vector of A then the eigen vector of the matrix B is

(a) P1 AX

(b) AX

(c) P1 X

(d) P1 AB

16. By Cayley-Hamilton theorem , matrix A =

2 41 1

, satisfies its characteristic equation. What is it?

(a) A2 + 3A - 2 = 0

(b) A2 + 3A + 2 = 0

(c) A2 - 3A + 2 = 0

(d) A2 - 3A - 2 = 0

17. The characteristic equation of the square matrix A =

2 37 4

is 2 + 2 + 13 = 0, then A1 is

(a)

1

13 4 37 2

(b) 1

13

4 37 2

(c) 113

4 37 2

(d) 113

4 37 2

18. If A =

4 13 2

then the diagonal matrix D =

(a) 1 0

0 1

(b)

1 00 5

(c)

5 0

0 1

(d)

5 00 1

19. Given A =

4 13 2

, P =

1 13 1

and D =

1 00 5

then the value of P1A4P =

(a)

1 00 625

(b)

1 00 5

(c)

1 00 125

(d)

1 00 25

20. If X1 =

310

, X2 =

114

and X3 =

210

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

(a)

3 1 01 1 1

0 4 0

(b)

3 1 21 1 2

0 4 0

(c)

3 1 21 1 1

0 4 0

(d) 3 1 21 1 10 4 0

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