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1. Example for scalar matrix is
(a)
1 0 3
0 3 2
0 0 4
(b)
2 0 0
0 2 2
0 2 2
(c)
2 0 0
0 2 00 0 2
(d)
2 0 0
0 3 0
0 0 4
2. If A =
0 4
0 0
, then A2 =
(a)
0 4
0 0
(b)
0 00 0
(c)
0 1
0 0
(d)
0 16
0 0
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) 4(b) 32
(c) 8
(d) 16
4. If A
0 1
2 1
=
0 4
0 0
, then A is
(a)
2 1
0 0
(b)
2 1
0
1
(c)
2 1
1 0
(d)
2 1
1/2 1/2
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
13
16 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) 2
(b) 1
(c) 5
(d) 3
7. L U decomposition method fails if lii = uii =
(a) 3
(b) 0
(c) 2
(d) 1
8. What is the rank of A =
1 2 3
2 3 4
3 4 6
(a) 2
(b) 0
(c) 1
(d) 3
9. For 4 5 matrix the sum of its rank and nullity is(a) 4
(b) 3
(c) 6
(d) 5
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 = 6 , b = 5(b) a = 4, b = 5(c) a = 3 , b = 5
(d) a = 5, b = 5
11. The characteristic roots of A =
1 02 5
are
(a) 1, 5
(b) 1, 2
(c) -1, 5
(d) 5, 3
12. The eigen values of A =
2 0
2 2
are
(a) 2, 0
(b) 2, -2
(c) -2, -2
(d) 2, 2
13. If 3 is the eigen value of A, then eigen value of A2 is
(a) 12
(b) 6
(c) 9
(d) 3
14. An eigen vector X of the equation AX = X can not correspond
to eigen value of the matrix A.
(a) more than one
(b) less than one
(c) more than two
(d) less than zero15. The sum of the eigen values of a matrix A
is equal to
(a) its value of the determinant
(b) trace of A
(c) its rank
(d) its nullity
16. The characteristic equation of the matrix A =
0 0 60 0 0
0 0 0
is
(a) 3
= 6(b) 3 + = 0
(c) 3 = 1
(d) 3 = 0
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) 64 I
(b) 16 I
(c) 4 I
(d) I
18. The diagonal matrix has the eigen values of A as its
elements
(a) diagonal
(b) positive
(c) real
(d) row
19. If1 , 2 , 3 are the eigen values of matrix A and An = BDnB1
then Dn =
(a)
n1
0 00 n
20
0 0 n3
(b)
1 0 00
20
0 0 3
(c)
n
10 0
0 n2
00 0 n
3
(d)
n
10 0
0 n2
00 0 n
3
20. The modal matrix is obtained by grouping the
(a) Eigen values into a square matrix
(b) Eigen vectors into a square matrix
(c) each column of the elements
(d) diagonal elements of a square matrix
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