Mathematics Matrices and Determinants Online Test

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Question 1

1. Trivial solution of homogeneous linear equation is

Question 2

2.

Question 3

3. If A and B are matrices, then which from the following is true?

Answer

A + B ≠ B + A

Answer

(A¹) ≠ A

Answer

All are true

Question 4

4.

Answer

Zero matrix

Answer

Identity matrix

Answer

Non – diagonal matrix

Answer

Row matrix

Question 5

5. (AB)t = ?

Question 6

6. The transpose of a row matrix is a

Answer

Zero matrix

Answer

Scalar matrix

Answer

Column matrix

Answer

Diagonal matrix

Question 7

7.

Answer

None of these

Question 8

8. If A is skew symmetric matrix, then Aᵗ =

Answer

Diagonal matrix

Question 9

9.

Then order of matrix A = ?

Question 10

10. A matrix having m rows and n columns with m ≠ n is said to be a

Answer

Rectangular matrix

Answer

Square matrix

Answer

Scalar matrix

Answer

Identity matrix

Question 11

11. A matrix A over the filed C in which (A)ᵗ is called

Answer

Hermitian matrix

Answer

Scalar matrix

Question 12

12. If a matrix has m rows and n columns then is order is

Question 13

13. The order of the matrix A is 3 x 5 and that of B is 2 x 3. The order of the matrix BA is

Question 14

14. Equation having a common solution are called

Answer

Linear equations

Answer

Homogeneous equations

Answer

None of these

Answer

Simultaneous equation

Question 15

15. A square matrix A = [aij] is supper triangular when

Answer

aij = 0 for all i > j

Question 16

16. Minimum number of equation for any system of equations

Answer

None of these

Question 17

17. If A = [aij] is (m x n) matrix, then transpose of A is of the order.

Question 18

18.

Answer

II & III only

Question 19

19.

Answer

Identity matrix

Answer

None of these

Answer

Diagonal matrix

Answer

Scalar matrix

Question 20

20.

Question 21

21. System of linear equations is inconsistent if:

Answer

System has no solution

Answer

System has one solution

Answer

None of these

Answer

System has two solutions

Question 22

22. The square matrix A is skew-symmetric when Aᵗ = 0

Question 23

23. If the order of matrix A is m x p. And the order of B is p x n. Then the order of AB is?

Question 24

24. Let A is a 3 x 3 matrix and B is its adjoint matrix. If |B| = 64, then |A| =

Question 25

25. The matrix A is Hermitian when (Ā)ᵗ =

Question 26

26.

Question 27

27. If A, B, and C are three matrices such that AB = C then which one is true?’ I = C/A, II = CA¯¹, III = A¯¹C

Answer

II and III

Question 28

28. For a square matrix A if A² = A then A is called

Answer

Periodic matrix

Answer

Idempotent matrix

Answer

Nilpotent matrix

Answer

Symmetric matrix

Question 29

29.

Question 30

30.

Question 31

31.

Question 32

32. If a system of equation has a unique solution or infinitely many solution then it is known as

Answer

Consistent

Answer

None of these

Answer

Inconsistent

Question 33

33. [-1, 4 7 2] is a

Answer

Column matrix

Answer

Diagonal matrix

Answer

Row matrix

Answer

Scalar matrix

Question 34

34. If a is matrix of order m x n and B is a matrix of order n x p then order of AB is

Question 35

35. An elementary row operation on a matrix A is

Answer

Interchange of any two rows of A

Answer

Multiplication of a column of a by any nonzero scalar

Answer

Interchange of any two columns of A

Answer

Addition of any multiple of one column to another column of A

Question 36

36. For any non-Singular r matrix A, A¯¹ =

Answer

None of these

Answer

1/|A|adj A

Question 37

37. The transpose of a square matrix is a

Answer

Square matrix

Answer

Scalar matrix

Answer

Diagonal matrix

Answer

Rectangular matrix

Question 38

38. A and B be two square matrices and if their inverse exist, the (AB)¯¹ =

Answer

A¯¹B¯¹

Answer

B¯¹A¯¹

Question 39

39. We solve the system of non-homogeneous linear equations by:

Answer

a, b and c

Question 40

40. Two matrices A and B are equal if

Answer

Both are rectangular

Answer

Number of columns of a is equal to number of rows of B

Answer

Both have same order

Answer

Both have same order and equal corresponding elements

Question 41

41. The leading diagonal or main diagonal of a square matrix known as

Answer

None of these

Answer

Both a and b

Answer

The principal diagonal

Answer

The secondary diagonal

Question 42

42.

Question 43

43. If B is additive inverse of A then

Question 44

44. If order of matrix A is 1 x 3 then orders of Aᵗ is

Question 45

45. If AB = BA = I and AC = CA = I then what about B and C.

Answer

Each is equal to A

Answer

None of these

Answer

They are equal

Answer

They are not equal

Question 46

46. If A and B are two matrices such that AB = B and BA = A, then A² + B² =

Question 47

47. If |A| = 0, then A is

Answer

Singular matrix

Answer

Zero matrix

Answer

Non- singular matrix

Question 48

48. The number of non-zero rows in an echlon form is called

Answer

Reduced echlon form

Answer

Rank of a matrix

Answer

Conjugate of the matrix

Answer

Cofactor of the matrix

Question 49

49.

Question 50

50.

Question 51

51. If A is null matrix, then A/|A| is

Question 52

52.

Answer

Scalar matrix

Answer

Diagonal matrix

Answer

Zero matrix

Answer

Column matrix

Question 53

53. If the trace of a matrix A is 5, then the trace of the matrix 3A is

Question 54

54. In matrix multiplication for A and B, (AB)ᵗ is

Question 55

55. Matrices A = [aij] 2 x 3 and B = [bij] 3 x 2 are suitable for

Question 56

56. A square matrix A = [aij] is lower triangular matrix when:

Answer

Aij = 0 for all i < j

Question 57

57. If A is a skew-symmetric matrix of order n and P, any square matrix of order n, prove that P’ AP is

Answer

Skew-symmetric

Question 58

58. The square matrix A is skew Hermitian when (Ā)ᵗ =

Question 59

59. [0 0 0] is

Answer

Identity matrix

Answer

Null matrix

Answer

Diagonal matrix

Answer

Scalar matrix

Question 60

60. (CD)ᵗ = ?

Question 61

61.

Question 62

62. For non-trival solution |A| is:

Question 63

63. For a square matrix A, if A = Aᵗ, then A is called:

Answer

Non-symmetric

Question 64

64. Let A = [aiJ]mxn I aj = 0 ∀i ≠ j and aj ≠ 0 for some 1 = j then matrix A is

Answer

Diagonal matrix

Answer

Symmetric matrix

Answer

None of these

Answer

Hermition matrix

Answer 94

b = 0, a = 0

Answer 95

a = 0, b ≠ 0

Answer 96

a = -0, a ≠ 0

Answer 97

a ≠ 0, b ≠ 0, k = 0

Answer 98

None of these

Answer 99

None of these

Answer 100

Number of columns of A is equal to number of rows of B

Answer 101

Both are rectangular

Answer 102

Number of rows of A is equal to number of columns of B

Answer 103

Both have same order

Answer 104

Even matrix

Answer 105

Scairar matrix

Answer 106

Identity matrix

Answer 107

Odd matrix

Answer 108

a = 3, b = 2

Answer 109

a = 3, b = 3

Answer 110

a = 2, b = 2

Answer 111

a = 2, b = 3

Answer 112

Skew-hermitian

Answer 113

Skew – symmetric

Answer 114

a, b and c

Answer 115

a₁₁, a₁₂, a₁₃

Answer 116

a₂₁, a₂₂, a₂₃

Answer 117

a₁₁, a₂₁

Answer 118

None of these

Answer 119

C’B’A’

Answer 120

None of the above

Answer 121

Skew-symmetric

Total Questions:	82
Time Allowed:	40 Minutes
Total Marks:	82
How to Attempt Test:	Please choose the right Option in MCQ-type question.
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