7/30/2019 mm-21
1/1
1. The matrix
28 49
16 28
is a matrix
(a) Nilpotent
(b) Skew-symmetric
(c) Orthogonal
(d) Involutary
2. A =
2 2 41 3 4
1 2 3
is
(a) Orthogonal
(b) Involutary
(c) Nilpotent
(d) Idempotent matrix
3. Find the value of x such that A is singular were A =
3 x 2 22 4 x 12 4 (1 + x)
(a) 2
(b) 4
(c) 5
(d) 3
4. A square matrix A is called orthogonal if
(a) AA1 = I
(b) A2 = A
(c) AT = A
(d) A = AT
5. If a matrix A is 4
3 and B is 3
5. The number of multiplication operations needed to calculate
the matrix
product AB are
(a) 64
(b) 65
(c) 61
(d) 60
6. Matrix A is said to be symmetric matrix ifAT =
(a) I
(b) -A
(c)AT
(d) A
7. If A is a zero matrix then R(A) =
(a) 0
(b) 1
(c) 2
(d) 3
8. A matrix is multiplied with a non - singular matrix then the
rank of the matrix is
(a) order of the matrix
(b) zero(c) one
(d) remaining same
9. For 4 5 matrix the sum of its rank and nullity is
(a) 3
(b) 6
(c) 4
(d) 5
10. The system A X = 0 possesses a non-zero solution if and only
if A is
(a) a non singular matrix
(b) a singular matrix
(c) a square matrix
(d) rectangular matrix
11. If A =
2 00 1
then the characteristic equation of A2 is
(a) 2 + 6 + 4 = 0
(b) 2 + 5 - 4 = 0
(c) 2 5 + 24 = 0
(d) 2 5 + 4 = 0
12. The eigen values of A =
2 0
2 2
are
(a) -2, -2
(b) 2, 0
(c) 2, 2
(d) 2, -2
13. If 3 is the eigen value of A, then eigen value of A2 is
(a) 9
(b) 3
(c) 6
(d) 12
14. If1, 2, 3 are the eigen values of A then the eigen values of
AT ane
(a) 1,2,3(b) 1, 2, 3
(c) -1,2,3(d) 1, 2,3
15. If X is an eigen vector of A corresponding to an eigen value
and k is any non zero scalar, then is an eigen
vector of A for the same eigen value .
(a) - X
(b) kX
(c) -kX
(d) X
16. If A =
1 42 3
, then by Cayley-Hamilton theorem A2 =
(a) 5A + 4I
(b) 4A + 5I
(c) - 4A - 5I(d) 4A - 5I
17. For the square matrix A, the characteristic equation is A3
4A2 - A + I = 0, then A1 is
(a) - A2 + 4A + I = 0
(b) A2 - 4A + I = 0
(c) A2 + 4A + I = 0
(d) A2 + 4A - I = 0
18. The matrix B, which diagonalise a matrix A, constitute the
vectors of A.
(a) eigen
(b) linear independent
(c) linear dependent
(d) Unit
19. If 2, 3, 4 are the eigen values of matrix A and A 3 = BD3B1
then D3 =
(a)
8 0 00 3 0
0 0 4
(b)
2 0 00 3 00 0 4
(c)
8 0 00 27 0
0 0 64
(d)
2 0 00 27 0
0 0 4
20. If X1 =
23
, X2 =
1 1
are the eigen vectors of A , then normalized modal matrix of A
is
(a) 213
12
3
13
12
(b)
213
12
313
12
(c)
213
12
313
12
(d)
213
12
313
12
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