1. If A is a square matrix of order 3 and |A| = 5 then |3A| = ?
(a) 135
(b) 45
(c) 15
(d) 32
Ans : (a) 135
2. Inverse of a matrix A exists, if
(a) | A | = 0
(b) Matrix A is non-singular
(c) Matrix A is singular
(d) AT = A
Ans : (b) Matrix A
is non-singular
3. If the value of then the value of
(a) -7
(b) 14
(c) 7
(d) -14
Ans : (c) 7
4. If matrix A = and A2 +
aA + b = O, then the values of a and b are:
(a) a = – 6, b = 2
(b) a = 6, b = – 2
(c) a = 6, b = 2
(d) a = – 6, b = – 2
Ans : (a) a = – 6, b = 2
5. I, then the relation between x and y
is
(a) y = -3x
(b) x = 3y
(c) x = -3y
(d) y = 3x
Ans : (d) y = 3x
6.
(a) −2(a+b+c)3
(b) 2(a+b+c)2
(c) 4(a+b+c)3
(d) None of these
Ans : (d) None of
these
7. The minor Mij of
an element aij of a determinant
is defined as the value of the determinant obtained after deleting the
(a) jth row of the determinant
(b) ith column and jth row of the determinant
(c) ith row and jth column of the determinant
(d) ith row of the determinant
Ans : (c) ith row and jth
column of the determinant
8. If A and B are any 2 × 2 matrices , then det. (A+B) = 0
implies
(a) det A = 0 and det B = 0
(b) det A = 0 or det B = 0
(c) detA + det B = 0
(d) None of these
Ans : (d) None of
these
9. If A = , and |3A| = k|A|, then the
value of k is
(a) 27
(b) 1
(c) 25
(d) 4
Ans : (a) 27
10. A system of linear equations AX = B is said to be
inconsistent, if the system of equations has
(a) Trivial Solution
(b) Infinite Solutions
(c) No Solution
(d) Unique Solutions
Ans : (c) No Solution
11. If A is a square matrix of order 3 and |A| = 7 then |AT| =
(a) 7
(b) 21
(c) 1/7
(d) 3
Ans : (a) 7
12. The value of the determinant is
(a) 4
(b) 0
(c) -1
(d) 1
Ans : (b) 0
13. System of equations AX = B is inconsistent if
(a) │B│ = 0
(b) (adj A) B = 0
(c) (adj A) B ≠ 0
(d) │A│ ≠ 0
Ans : (c) (adj A) B ≠ 0
14. Points (a,a,c),(1,0,1) and (c,c,b) are collinear if
(a) a,b,c in GP
(b) a,b,c in AP
(c) C2 = ab
(d) C = ab
Ans : (c) C2 = ab
15. If I3 is the
identity matrix of order 3 , then 13−1 is
(a) 0
(b) 3I3
(c) I3
(d) None of these
Ans : (c) I3
16. The following system of equations has
x + 3y + 3z = 2
x + 4y + 3z = 1
x + 3y + 4z = 2
(a) Infinite Solution
(b) Trivial Solution
(c) Unique Solution
(d) No Solution
Ans : (c) Unique Solution
17. In a third order determinant, each element of the first column
consists of sum of two terms, each element of the second column consists of sum
of three terms and each element of the third column consists of sum of four
terms. Then it can be decomposed into n determinants, where n has value
(a) 1
(b) 9
(c) 24
(d) 16
Ans : (c) 24
18. The value of determinant
(a) zero
(b) 8
(c) 1
(d) 10
Ans : (a) zero
19. The system of equations kx + 2y – z = 1,
(k – 1)y – 2z = 2
(k + 2)z = 3 has a unique solution, if k is
(a) – 1
(b) – 2
(c) 1
(d) 0
Ans : (a) – 1
20. If A is a symmetric matrix, then At =
(a) A
(b) |A|
(c) 0
(d) diagonal matrix
Ans : (a) A
21. If A’ is the transpose of a square matrix A , then
(a) |A| ≠ |A′|
(b) |A|+|A′| = 0
(c) |A| = |A′|
(d) None of these
Ans : (c) |A| = |A′|
22. If A B be two square matrices such that AB = O, then
(a) Det.B = 0
(b) BA
(c) Det. A = 0 or Det. B = 0
(d) Det. = A = 0
Ans : (c) Det. A = 0 or
Det. B = 0
21.
(a) A2=A
(b) A3 = A
(c) A2 = O
(d) None of these
Ans : (c) A2 =
O
22. For a skew symmetric even ordered matrix A of integers,
which of the following will not hold true:
(a) det(A) = 9
(b) det(A) = 81
(c) det(A) = 7
(d) det(A) = 4
Ans : (c) det(A) = 7
23. If A any square matrix then which of the following is not
symmetric ?
(a) A−At
(b) A+At
(c) AAt
(d) AtA
Ans : (a) A−At
24. For what value of λ the following system of equations does
not have a solution ?
x + y + z = 6, 4x + λy - λz = 0, 3 x + 2y – 4 z = - 5
(a) 0
(b) 3
(c) -3
(d) 1
Ans : (b) 3
25. A square matrix A = [aij]n×n is called a diagonal matrix if
aij = 0 for
(a) I < j
(b) I = j
(c) I > j
(d) I ≠ j
Ans : (d) I ≠ j
26. The number of all possible matrices of order 3×3 with each
entry 0 if 1 is
(a) 81
(b) 512
(c) 18
(d) None of these
Ans : (b) 512
27. The system of equations, x + y + z = 1, 3 x + 6 y + z = 8,
αx + 2 y + 3z = 1 has a unique solution for
(a) α not equal to 0
(b) all integral α
(c) all rational α
(d) all real α
Ans : (b) all integral α
28. The inverse of a matrix is defined for
(a) Only square matrices
(b) Diagonal matrices
(c) all matrices
(d) Rectangular matrices
Ans : (a) Only
square matrices
29. If A is any square matrix, then
(a) A+At is symmetric
(b) A−At is symmetric
(c) A+At is skew-symmetric
(d) None of these
Ans : (a) A+At is
symmetric
30. If A is a matrix of order 1×3 and B is a matrix of order
3×4, then order of the matrix obtained on multiplying A and B is
(a) 3×3
(b) 4×1
(c) 3×4
(d) 1×4
Ans : (d) 1×4
31. If A is a matrix of order 3 × 4 , then each row of A has
(a) 12 elements
(b) 3 elements
(c) 4 elements
(d) 7 elements
Ans : (c) 4 elements
32. For a skew symmetric even ordered matrix A of integers,
which of the following will not hold true:
(a) det(A) = 9
(b) det(A) = 81
(c) det(A) = 7
(d) det(A) = 4
Ans : (c) det(A) = 7
33. If a square matrix A has two identical rows or columns ,
then det.A is :
(a) 0
(b) -1
(c) 1
(d) None of these
Ans : (a) 0
34. The equations x + 2y + 2z = 1 and 2x + 4 y + 4z = 9 have
(a) infinitely many solutions.
(b) only one solution
(c) only two solutions
(d) no solution
Ans : (d) no
solution
35. Then the value of x is ____
(a) 6
(b) 3
(c) 2
(d) 0
Ans : (b) 3
36. Matrix A when multiplied with Matrix C gives the Identity matrix
I, what is C?
(a) Identity matrix
(b) Inverse of A
(c) Square of A
(d) Transpose of A
Ans : (b) Inverse of A
37. square matrix A = [aij]n×n is called a lower
triangular matrix if aij = 0 for
(a) i is less than j
(b) i = j
(c) iis greater than j
(d) None of these
Ans : (a) i is less than
j
38. If A and B are two matrices conformable to multiplication
such that their product
AB = O(Zero matrix). Then which of the following is true
(a) A and B are both null matrices
(b) Either of A is or B is a null matrix
(c) Neither of them may be a zero matrix
(d) All of the above options are correct
Ans : (d) All of the
above options are correct
39. The system of linear equations
x + y + z = 2, 2x + y - z = 3, 3x + 2y - kz = 4 has a unique
solution if ,
(a) k = 0
(b) − 1 < k < 1
(c) − 2 < k < 2
(d) k ≠ 0
Ans : (d) k ≠ 0
40. What is the element in the 2nd row and 1st column of a 2 x 2
Matrix A = [ aij], such that a = (i + 3) (j – 1)
(a) 0
(b) 4
(c) -5
(d) 5
Ans : (a) 0
41. If the system of equations
x + 4 ay + az = 0, x + 3by + bz = 0 and
x + 2 cy +cz = 0 have a non-zero solution,then a, b, c are in
(a) H.P.
(b) G.P.
(c) A.P.
(d) None of these
Ans : (a) H.P.
42. Rank of a non-zero matrix is always
(a) ⩾1
(b) 0
(c) greater than 1
(d) equal to 1
Ans : (a) ⩾1
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