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1. A square matrix is said to be lower triangular matrix if

(a) aij = 0 , i < j

(b) aij = 0, i = j

(c) aij = 0 , i > j

(d) aij = 1, i = j

2. If A =

2 0 0

0 3 0

0 0 4

then Am =

(a)

2m 0 0

0 3m 0

0 0 4m

(b)

2m 0 0

0 3m 0

0 0 4m

(c)

2 0 0

0 3 0

0 0 4

(d)

2 + m 0 00 3 + m 00 0 4 + m

3. If A =

2 0 0

0 2 0

0 0 2

and B =

1 2 3

0 1 3

0 0 2

then det of AB has the value

(a) 32

(b) 8

(c) 16

(d) 4

4. If

5 4

1 1

=

1 2

1 3

, then equals to

(a)

3 14

4 17

(b)

3 14

5 17

(c)

3 14

4 17

(d) 3 14

4 17

5. The matrix

0 6

0 0

is a matrix

(a) Skew-symmetric

(b) Nilpotent

(c) Involutary

(d) Orthogonal

6. If A =

1 2

2 3

, then (A + AT)2 =

(a)

2 0

0 6

(b)

4 0

0 6

(c)

4 0

0 12

(d)

4 0

0 36

7. L U decomposition method fails if lii = uii =

(a) 2

(b) 0

(c) 3

(d) 1

8. The system of equations x + 2y - 3z = 0 , 2x - y + 2z = 0, x + 7y - 11z = 0 is

(a) consistent

(b) unique solution

(c) no solution

(d) In consistent

9. If

1 0 1 20 0 2 4

0 0 3 10

which is an Echelon form of the given system of

equations, then the system of equations has infinite number of solutions if

(a) = 8, = 10

(b) = 3, = 10

(c) = 3, = 10

(d) = 3, = 10

10. The solution of system of equations x + y + z = 1 , 2x + 3y + 2z = 2, 5x + 4y + 3z = 3 is

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

(b) x = y = z = 1

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

(d) x = y = z = 0

11. Characteristic equation of A =

2 2 72 1 2

0 1 3

is

(a) 315+12 = 0

(b) 313+12 = 0

(c) 3

1312 = 0(d) 3+15+12 = 0

12. If A =

1 00 5

then the eigen values of A2 are

(a) 1, 25

(b) -1, -5

(c) 1, -2

(d) 1, 5

13. If one of the eigen values of A is zero, then A is

(a) non-singular(b) skew - symmetric

(c) symmetric

(d) singular

14. The eigen vector corresponding to the eigen value = -2 for the matrix

1 1 01 1 0

0 0 5

is

(a) ( k, -k, 1 )

(b) (k, 0, 0 )

(c) (k, k, 0 )

(d) ( 0, 0, 0 )

15. The eigen vector corresponding to the eigen value is

(a) independent

(b) not unique

(c) unique

(d) Dependent

16. For the square matrix A =

3 0 05 4 03 6 1

, then A3 - 8A2 + 19A =

(a) 20 I

(b) I

(c) 12 I

(d) 13 I

17. If the characteristic equation of the square matrix A is 2 - 4 = 0 then A4 =( where I is the second order unit matrix )

(a) I

(b) 64 I

(c) 16 I

(d) 4 I

18. Diagonalization of a matrix by orthogonal transformation is possible only for matrix.

(a) skew-symmetric

(b) symmetric

(c) orthogonal

(d) real symmetric

19. Given A =

4 13 2

, P =

1 13 1

and D =

1 00 5

then the value of P1A4P =

(a) 1 0

0 125

(b)

1 00 625

(c)

1 00 5

(d)

1 00 25

20. If B is the modal matrix of A , then B is formed whose columns are the of A

(a) eigen values

(b) eigen vectors(c) normalized eigen vectors

(d) elements

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