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

(a) skew symmetric

(b) unit matrix

(c) nilpotent

(d) symmetric

2. If A =

1 a

0 1

what is An ? where n is positive integer.

(a) 1 na

0 1

(b)

1 an

0 1

(c)

1 0

0 1

(d)

na 0

0 1

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

(a)

AT

(b) -A

(c) A

(d) I

4. If A

0 1

2 1

=

0 4

0 0

, then A is

(a)

2 1

1 0

(b)

2 1

0 1

(c)

2 10 0

(d)

2 1

1/2 1/2

5. If the matrix A =

2 3

5 1

is expressed as the sum of a symmetric and a skew symmetric. Then the skew -

symmetric matrix is

(a)

0 11 0

(b) 2 1

2 4

(c)

2 4

4 1

(d)

4 2

2 1

6. If A =

1 2

2 3

, then (A + AT)2 =

(a)

4 0

0 6

(b)

2 0

0 6

(c)

4 0

0 36

(d)

4 0

0 12

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

(a) Number of non - zero rows

(b) Number of non-zero elements

(c) Number of non zero -columns(d) Number of diagonal elements

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

(a) In consistent

(b) no solution

(c) unique solution

(d) consistent

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

(a) unique solution

(b) consistent

(c) no solution

(d) In consistent

10. For what values of a and b the equation x + 2y + 3z = 4 , x - 3y + 4z = 5, x + 3y + az = b has no solution.

(a) a = 5, b = 5

(b) a = 3 , b = 5

(c) a = 6 , b = 5(d) a = 4, b = 5

11. Characteristic equation of A = 2 2 72 1 2

0 1 3 is

(a) 31312 = 0(b) 3+15+12 = 0

(c) 315+12 = 0(d) 313+12 = 0

12. If A =

1 00 5

then the eigen values of A2 are

(a) 1, 5

(b) -1, -5

(c) 1, 25

(d) 1, -2

13. If A =

1 3 10 2 6

0 0 3

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

(a) 11

(b) 6

(c) 10

(d) 12

14. The normalized form of eigen vector for

21

1

is

(a) 1/

6

21

1

(b) 1/

6

21

1

(c) 1/6 211

(d) 1/

6

21

1

15. If X1 and X2 are two eigen vectors of a matrix A corresponding to the same eigen value of A then any linearcombination of the form isalso gives eigen vector of A corresponding to the same eigen value

(a) X1 + X2

(b) k1X1 + k2X2

(c) X1X2

(d) k1X1 k2X2

16. For the square matrix A =

3 0 05 4 0

3 6 1

, then A3 - 8A2 + 19A =

(a) I

(b) 13 I

(c) 20 I

(d) 12 I

17. The inverse of the matrix A = 5 33 2

is

(a)

2 33 5

(b)

2 35 3

(c)

5 31 2

(d)

5 41 2

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

(a) orthogonal

(b) real symmetric

(c) symmetric

(d) skew-symmetric

19. If D = P1A P, then D10 =

(a) P1A10 P

(b) P1PA10

(c) A4PP1

(d) PA10P1

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 row by sum of the diagonal elements

(d) each column by length of a vector

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