1. A matrix A for which AP = 0 where P is a positive integer is called
(a) skew symmetric
(b) unit matrix
(c) symmetric
(d) nilpotent
2. If A = 0 4
0 0, then A2 =
(a) 0 1
0 0
(b) 0 0
0 0
(c) 0 16
0 0
(d) 0 4
0 0
3. If A = 3 − 4
1 − 1 then An is
(a) 2n − 4n + 1
n 1 − 2n
(b) 1 + 2n − 4n
n 1 − 2n
(c) 1 + 3n − 4n
n 1 + 2n
(d) 1 + 3n − 4n
n 1 − 2n
4. If 1 − k 2
3 1 + k + A= 2 0
0 2 , then A =
(a) 1 − k − 2
−3 1 + k
(b) 1 + k 2
−3 1 − k
(c) 1 + k 2
3 1 − k
(d) 1 + k − 2
−3 1 − k
5. The matrix 0 6
0 0 is a matrix
(a) Involutary
(b) Nilpotent
(c) Orthogonal
(d) Skew-symmetric
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. The rank of a matrix A = 264
1 2 3
0 x 4
1 − 1 1
375
is 2, then the value of x is
(a) 5
(b) 3
(c) 6
(d) 4
9. The value of x and y, if 0 − 1
1 0 x
y = 5
4
(a) x = 4 , y = -5
(b) x = 4 , y = 5
(c) x = 4 , y = 3
(d) x = 1 , y = 2
10. If A is a non singular matrix then the linear system AX = 0 has only
(a) the zero solution
(b) a non-zero solution
(c) infinite solution
(d) unique solution
11. Characteristic equation of A = 24
2 2 − 7
2 1 2
0 1 − 3 35 is
(a) 3+15+12 = 0
(b) 3−13−12 = 0
(c) 3−13+12 = 0
(d) 3−15+12 = 0
12. Eigen values of A = 1 0
3 2 are
(a) 1,2
(b) 2,3
(c) - 1, -2
(d) 0,1
13. If one of the eigen values of A is zero, then A is
(a) singular
(b) skew - symmetric
(c) non-singular
(d) symmetric
14. The normalized eigen vector corresponding to the eigen value = 2 for the vector ( 2, 1) is
(a) (-2/p5, 1/p5 )
(b) (1/p5, 1/p5 )
(c) (2/ p5, 1/p5 )
(d) (2/p5,−1/p5 )
15. The eigen vector corresponding to the eigen value is
(a) independent
(b) Dependent
(c) not unique
(d) unique
16. The characteristic equation of a square matrix A is 3 − 32 − 7 - 11 = 0, then A−2 =
(a) 1
11[A + 7A−1+3I] = 0
(b) 1
11[A + 7A−1−3I] = 0
(c) 1
11[A − 7A−1+3I] = 0
(d) 1
11[A − 7A−1−3I] = 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) 16 I
(b) 4 I
(c) I
(d) 64 I
18. The diagonal matrix has the eigen values of A as its elements
(a) positive
(b) diagonal
(c) row
(d) real
19. Given A = 4 1
3 2 , P = 1 1
−3 1 and D = 1 0
0 5 then the value of P−1A4P =
(a) 1 0
0 125
(b) 1 0
0 25
(c) 1 0
0 625
(d) 1 0
0 5
20. If D is the diagonal matrix with eigen values of A as the principal diagonal elements then D is
(a) spectral matrix
(b) Model matrix
(c) Null matrix
(d) Unit matrix
D B B D B A B C B A C A A C C D A B C A
1. A square matrix is said to be lower triangular matrix if
(a) aij = 0 , 8 i > j
(b) aij = 0, 8 i = j
(c) aij = 0 , 8 i < j
(d) aij = 1, 8 i = j
2. (AB)−1 =
(a) (BA)−1
(b) B−1A−1
(c) −B−1A−1
(d) A−1B−1
3. Matrix A is said to be skew - symmetric matrix if AT =
(a) −AT
(b) -A
(c) I
(d) A
4. If A 0 1
2 − 1 = 0 4
0 0 , then A is
(a) 2 1
1 0
(b) 2 1
−1/2 − 1/2
(c) 2 1
0 − 1
(d) 2 1
0 0
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) 2 1
2 4
(b) 4 2
2 − 1
(c) 0 − 1
1 0
(d) 2 4
4 1
6. If A = 1 2
2 1, B = 1 1
1 1, then AB is
(a) 2 2
2 2
(b) 1 1
1 1
(c) 4 4
4 4
(d) 3 3
3 3
7. L U decomposition method fails if lii = uii =
(a) 2
(b) 1
(c) 3
(d) 0
8. The system of equations AX = B has an infinite number of solution if
(a) R(AB) = R(A) = r = n
(b) R(AB) = R(A) = r > n
(c) R(AB) 6= R(A) > n
(d) R(AB) = R(A) = r < n
9. If every minor of order r of a matrix A is non-zero, then rank of A is
(a) equal to r
(b) greater than or equal to r
(c) less than r
(d) less than or equal to r
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 = 0 , y = 0 , z = 1
(c) x = y = z = 0
(d) x = y = z = 1
11. Characteristic equation of A = 24
1 1 − 2
−1 2 1
0 1 − 1 35 is
(a) 3+22−3+2 = 0
(b) 3+22−+2 = 0
(c) 3+22+3+2 = 0
(d) 3−22−+2 = 0
12. If A = 1 0
0 5 then the eigen values of A2 are
(a) -1, -5
(b) 1, -2
(c) 1, 5
(d) 1, 25
13. The eigen values of A−1 , where A = 24
2 7 6
0 4 1
0 0 5 35 are
(a) -1/2, -1/4, 1/5
(b) 1/2, 1/4, 1/5
(c) 2, 4, 5
(d) 1/2, 1/4, -1/5
14. If X = 24
x1
x2
x3
35
be the eigen vector corresponding to the eigen value , then
( A - I) X=
(a) I
(b) - 1
(c) 1
(d) 0
15. If X1 and X2 are two eigen vectors of a matrix A corresponding to the same eigen value of A then any linear
combination of the form isalso gives eigen vector of A corresponding to the same eigen value
(a) k1X1 + k2X2
(b) X1 + X2
(c) X1 − X2
(d) k1X1 − k2X2
16. The characteristic equation of a square matrix A is 3 − 32 − 7 - 11 = 0, then A−2 =
(a) 1
11[A − 7A−1−3I] = 0
(b) 1
11[A + 7A−1−3I] = 0
(c) 1
11[A + 7A−1+3I] = 0
(d) 1
11[A − 7A−1+3I] = 0
17. If 1, 2, 3 are the latent roots of a square matrix A , then the latent roots of A2 are
(a) −1
2,2
2,3
2
(b) −1/1,−1/2, 1/3
(c) 1/1, 1/2, 1/3
(d) 1
2,2
2,3
2
18. The diagonal matrix has the eigen values of A as its elements
(a) positive
(b) real
(c) diagonal
(d) row
19. If the eigen vector of A is X = 1
−2 then eigen vector of A2 is
(a) X3
(b) X2
(c) - X2
(d) X
20. The matrix B which diagonalises A is matix.
(a) modal
(b) spectral
(c) Orthogonal
(d) symmetric
C B B B C D D D B B D D B D A A D C D A
