Mathematics Matrices and Determinants Online Test

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Question 1

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

Answer

None of these

Answer

The principal diagonal

Answer

Both a and b

Answer

The secondary diagonal

Question 2

2. Trival solution of homogeneous linear equation is:

Answer

a, b and c

Question 3

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

Answer

None of these

Answer

Consistent

Answer

Inconsistent

Question 4

4. Matrix obtained by interchanging its rows and columns is called

Answer

None of these

Question 5

5. 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 6

6. Trivial solution of homogeneous linear equation is

Question 7

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

Question 8

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

Answer

Non- singular matrix

Answer

Zero matrix

Answer

Singular matrix

Question 9

9. 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

Diagonal matrix

Answer

Hermition matrix

Answer

Symmetric matrix

Question 10

10. If for the matrix A, A⁵ = I, then A¯¹ =

Answer

None of these

Question 11

11. $Math 3. 04$

Answer

Skew-hermitian

Answer

Skew – symmetric

Question 12

12. [-1, 4 7 2] is a

Answer

Diagonal matrix

Answer

Column matrix

Answer

Scalar matrix

Answer

Row matrix

Question 13

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

Answer

aij = 0 for all i > j

Question 14

14. $Math 3. 18$

Question 15

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

Answer

A + B ≠ B + A

Answer

All are true

Answer

(A¹) ≠ A

Question 16

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

Question 17

17. $Math 3. 01$

Question 18

18. $Math 3. 08$

Question 19

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

Answer

Non-symmetric

Question 20

20. $Math 3. 12$

Answer

None of these

Answer

Identity matrix

Answer

Scalar matrix

Answer

Diagonal matrix

Question 21

21. (CD)ᵗ = ?

Question 22

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

Question 23

23. (ABC)’ =

Answer

C’B’A’

Question 24

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

Question 25

25. $Math 3. 16$

Question 26

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

Answer

B¯¹A¯¹

Answer

A¯¹B¯¹

Question 27

27. $Math 3. 15$

Answer

Identity matrix

Answer

Zero matrix

Answer

Row matrix

Answer

Non – diagonal matrix

Question 28

28. If A is non – singular matrix then (A¯¹)¯¹ = ?

Question 29

29. Two matrices A and B are equal if

Answer

Both have same order

Answer

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

Answer

Both have same order and equal corresponding elements

Answer

Both are rectangular

Question 30

30. Equation having a common solution are called

Answer

Linear equations

Answer

None of these

Answer

Simultaneous equation

Answer

Homogeneous equations

Question 31

31. [0 0 0] is

Answer

Identity matrix

Answer

Diagonal matrix

Answer

Null matrix

Answer

Scalar matrix

Question 32

32. $Math 3. 05$

Question 33

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

Answer

Aij = 0 for all i < j

Question 34

34. (AB)t = ?

Question 35

35. System of linear equations is inconsistent if:

Answer

System has no solution

Answer

System has two solutions

Answer

System has one solution

Answer

None of these

Question 36

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

Answer

Idempotent matrix

Answer

Nilpotent matrix

Answer

Symmetric matrix

Answer

Periodic matrix

Question 37

37. Two matrix A and B can be added if

Answer

Both are rectangular

Answer

Both have same order

Answer

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

Answer

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

Question 38

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

Answer

Diagonal matrix

Question 39

39. $Math 3. 02$

Question 40

40. $Math 3. 20$

Answer

None of these

Question 41

41. $Math 3. 17$

Answer

a₂₁, a₂₂, a₂₃

Answer

a₁₁, a₁₂, a₁₃

Answer

a₁₁, a₂₁

Answer

None of these

Question 42

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

Question 43

43. For trival solution |A| is:

Question 44

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

Question 45

45. $Math 3. 13$

Answer

Scalar matrix

Answer

Diagonal matrix

Answer

Column matrix

Answer

Zero matrix

Question 46

46. $Math 3. 11$

Answer

II & III only

Question 47

47. The additive inverse of a matrix A is

Question 48

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

Answer

1/|A|adj A

Answer

None of these

Question 49

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

Question 50

50. $Math 3. 21$

Question 51

51. If B is additive inverse of A then

Question 52

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

Question 53

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

Question 54

54. $Math 3. 03$ Then order of matrix A = ?

Question 55

55. 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 56

56. $Math 3. 06$

Answer

Scairar matrix

Answer

Even matrix

Answer

Identity matrix

Answer

Odd matrix

Question 57

57. $Math 3. 23$

Answer

a = 2, b = 2

Answer

a = 3, b = 3

Answer

a = 3, b = 2

Answer

a = 2, b = 3

Question 58

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

Answer

Reduced echlon form

Answer

Cofactor of the matrix

Answer

Conjugate of the matrix

Answer

Rank of a matrix

Question 59

59. $Math 3. 07$

Question 60

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

Question 61

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

Question 62

62. $Math 3. 19$

Question 63

63. 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 64

64. The transpose of a square matrix is a

Answer

Scalar matrix

Answer

Diagonal matrix

Answer

Rectangular matrix

Answer

Square matrix

Answer 96

Scalar matrix

Answer 97

Column matrix

Answer 98

Diagonal matrix

Answer 99

Zero matrix

Answer 100

None of the above

Answer 101

Skew-symmetric

Answer 102

Each is equal to A

Answer 103

None of these

Answer 104

They are equal

Answer 105

They are not equal

Answer 106

Identity matrix

Answer 107

Square matrix

Answer 108

Scalar matrix

Answer 109

Rectangular matrix

Answer 110

a ≠ 0, b ≠ 0, k = 0

Answer 111

b = 0, a = 0

Answer 112

a = -0, a ≠ 0

Answer 113

a = 0, b ≠ 0

Answer 114

Hermitian matrix

Answer 115

Scalar matrix

Answer 116

None of these

Answer 117

a, b and c

Answer 118

Interchange of any two rows of A

Answer 119

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

Answer 120

Interchange of any two columns of A

Answer 121

Multiplication of a column of a by any nonzero scalar

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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