1. A matrix A for which AP  = 0 where P is a positive integer is called

(a) unit matrix

(b) nilpotent

(c) symmetric

(d) skew symmetric

2. Let A be an n × n skew-symmetric matrix then A+AT  =

(a) 0

(b) 2AT 

(c) 1

(d) 2A

3. (AB)T  =

(a) (A+B)T 

(b) BT AT 

(c) AT B

T 

(d) −AT B

T 

4. A square matrix A is called orthogonal if 

(a) AT  = A

(b) A = AT 

(c) AA−1 = I

(d) A2 = A

5. If Am×n and B p×q are two matrices state the conditions for the existence of AB

(a) n = p

(b) n<p

(c) n=p

(d) n>p

6. A square matrix is said to upper triangular matrix if 

(a) aij = 0 , ∀ i < j

(b) aij = 0, ∀ i = j

(c) aij = 1 , ∀ i = j

(d) aij = 0 , ∀ i > j

7. The rank of a matrix in Echelon form is equal to

(a) Number of non - zero rows

(b) Number of diagonal elements

(c) Number of non-zero elements

(d) Number of non zero -columns

8. If A = LU, then A−1 =

(a) U −1L−1

(b) L−1U −1

(c) 1/ (LU)

(d) (LU )−1

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

(a) unique solution

(b) In consistent

(c) no solution

(d) consistent

10. The system 2x + y + z = 0 , x + y + 3z = 0 and 4x + 3y +λz = 0 has trivial solution then

(a) λ = 8

(b) λ = 6

(c) λ = 8

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(d) λ = 6

11. The eigen values of A =

−1 6 80 1 80 0 7

are

(a) -1, 2, 3

(b) 1, 2, 3

(c) - 1, 1, 7

(d) 1, 1, 7

12. The product of the eigen values of A =

1 2 00 1 50 0 2

is

(a) -1

(b) 1

(c) 2

(d) -2

13. If A =

1 3 10 2 60 0 3

then the sum of the eigen values of A and AT  is

(a) 12

(b) 6

(c) 10

(d) 11

14. The eigen vector corresponding to the eigen value λ = 1 for the matrix

1 2 30 −4 70 0 7

is

(a) ( 1, 1, 1 )

(b) (k, 0, 0 )

(c) (0, k, 0 )

(d) ( 0, 0, 0 )

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) P−1 X

(b) AX

(c) P−1 AB

(d) P−1 AX

16. By Cayley Hamilton theorem, matrix A =

5 41 2

, satisfies its characteristic equation. Which is

(a) A2 - 7A + 6 = 0

(b) A2 - 7A - 6 = 0

(c) A2 - 7A+ 2 = 0

(d) A2 - 7A - 2 = 0

17. If A =

1 22 − 1

, then by Cayley- Hamilton theorem, A8 is

(a)

624 00 624

(b)

626 00 626

(c)

625 00 625

(d)

623 0

(a)

0 1

(b)

6 00 1

(c)

−6 00 1

(d)

6 00 − 1

19. If D = B−1 AB , where D is the diagonal matrix then An =

(a) (B−1DB)n

(b) B DnB−1

(c) (B D B−1)n

(d) B−1Dn B

20. The normalized modal matrix is obtained by dividing

(a) each column by sum of the diagonal elements

(b) each row by length of a vector

(c) each column by length of a vector

(d) each row by sum of the diagonal elements