Mathematics Matrices and Determinants Online Test

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Question 1

1.

Question 2

2. Equation having a common solution are called

Answer

None of these

Answer

Simultaneous equation

Answer

Homogeneous equations

Answer

Linear equations

Question 3

3. System of linear equations is inconsistent if:

Answer

None of these

Answer

System has one solution

Answer

System has no solution

Answer

System has two solutions

Question 4

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

Answer

Square matrix

Answer

Identity matrix

Answer

Scalar matrix

Answer

Rectangular matrix

Question 5

5.

Answer

Skew – symmetric

Answer

Skew-hermitian

Question 6

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

Answer

Diagonal matrix

Question 7

7.

Question 8

8. 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 9

9. Two matrices A and B are equal if

Answer

Both are rectangular

Answer

Both have same order and equal corresponding elements

Answer

Both have same order

Answer

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

Question 10

10. 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 11

11.

Answer

a = 2, b = 3

Answer

a = 2, b = 2

Answer

a = 3, b = 2

Answer

a = 3, b = 3

Question 12

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

Question 13

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

Question 14

14. [0 0 0] is

Answer

Identity matrix

Answer

Diagonal matrix

Answer

Null matrix

Answer

Scalar matrix

Question 15

15. The transpose of a square matrix is a

Answer

Diagonal matrix

Answer

Rectangular matrix

Answer

Scalar matrix

Answer

Square matrix

Question 16

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

Question 17

17. The transpose of a row matrix is a

Answer

Column matrix

Answer

Diagonal matrix

Answer

Zero matrix

Answer

Scalar matrix

Question 18

18.

Question 19

19.

Question 20

20. Minimum number of equation for any system of equations

Answer

None of these

Question 21

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

Question 22

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

Question 23

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

Answer

Cofactor of the matrix

Answer

Rank of a matrix

Answer

Reduced echlon form

Answer

Conjugate of the matrix

Question 24

24.

Question 25

25. 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 26

26.

Question 27

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

Question 28

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

Answer

A¯¹B¯¹

Answer

B¯¹A¯¹

Question 29

29.

Question 30

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

Question 31

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

Answer

Symmetric matrix

Answer

Nilpotent matrix

Answer

Idempotent matrix

Answer

Periodic matrix

Question 32

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

Question 33

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

Answer

Aij = 0 for all i < j

Question 34

34.

Answer

II & III only

Question 35

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

Answer

They are equal

Answer

Each is equal to A

Answer

They are not equal

Answer

None of these

Question 36

36. (CD)ᵗ = ?

Question 37

37. Trival solution of homogeneous linear equation is:

Answer

a, b and c

Question 38

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

Answer

1/|A|adj A

Answer

None of these

Question 39

39.

Answer

Diagonal matrix

Answer

Scalar matrix

Answer

None of these

Answer

Identity matrix

Question 40

40. Trivial solution of homogeneous linear equation is

Question 41

41. An elementary row operation on a matrix A is

Answer

Interchange of any two rows of A

Answer

Interchange of any two columns of A

Answer

Multiplication of a column of a by any nonzero scalar

Answer

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

Question 42

42. 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 43

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

Answer

Non- singular matrix

Answer

Singular matrix

Answer

Zero matrix

Question 44

44.

Question 45

45. Let A be a square matrix. Then, ½ (A – A) is

Answer

Skew-symmetric

Answer

None of the above

Question 46

46.

Answer

Diagonal matrix

Answer

Scalar matrix

Answer

Zero matrix

Answer

Column matrix

Question 47

47. (AB)t = ?

Question 48

48.

Question 49

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

Question 50

50.

Answer

Even matrix

Answer

Identity matrix

Answer

Odd matrix

Answer

Scairar matrix

Question 51

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

Answer

The principal diagonal

Answer

The secondary diagonal

Answer

None of these

Answer

Both a and b

Question 52

52. (ABC)’ =

Answer

C’B’A’

Question 53

53.

Question 54

54.

Then order of matrix A = ?

Question 55

55. For trival solution |A| is:

Question 56

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

Question 57

57.

Answer

Row matrix

Answer

Non – diagonal matrix

Answer

Zero matrix

Answer

Identity matrix

Question 58

58. 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 59

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

Question 60

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

Question 61

61.

Question 62

62.

Answer

None of these

Question 63

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

Answer

a, b and c

Question 64

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

Answer

None of these

Answer

Symmetric matrix

Answer

Hermition matrix

Answer

Diagonal matrix

Answer 94

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

Answer 95

Both are rectangular

Answer 96

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

Answer 97

Both have same order

Answer 98

None of these

Answer 99

a = 0, b ≠ 0

Answer 100

b = 0, a = 0

Answer 101

a = -0, a ≠ 0

Answer 102

a ≠ 0, b ≠ 0, k = 0

Answer 103

All are true

Answer 104

(A¹) ≠ A

Answer 105

A + B ≠ B + A

Answer 106

Consistent

Answer 107

None of these

Answer 108

Inconsistent

Answer 109

Non-symmetric

Answer 110

None of these

Answer 111

a₁₁, a₂₁

Answer 112

a₁₁, a₁₂, a₁₃

Answer 113

None of these

Answer 114

a₂₁, a₂₂, a₂₃

Answer 115

Diagonal matrix

Answer 116

Row matrix

Answer 117

Scalar matrix

Answer 118

Column matrix

Answer 119

Hermitian matrix

Answer 120

Scalar matrix

Answer 121

aij = 0 for all i > j

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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