Mathematics Matrices and Determinants Online Test

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Question 1

1.

Then order of matrix A = ?

Question 2

2. 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 3

3. 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 4

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

Answer

1/|A|adj A

Answer

None of these

Question 5

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

Question 6

6. Equation having a common solution are called

Answer

Linear equations

Answer

None of these

Answer

Simultaneous equation

Answer

Homogeneous equations

Question 7

7. Trival solution of homogeneous linear equation is:

Answer

a, b and c

Question 8

8.

Question 9

9.

Answer

Column matrix

Answer

Zero matrix

Answer

Diagonal matrix

Answer

Scalar matrix

Question 10

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

Answer

None of these

Answer

Each is equal to A

Answer

They are equal

Answer

They are not equal

Question 11

11. For trival solution |A| is:

Question 12

12.

Question 13

13. Two matrices A and B are equal if

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

Answer

Both are rectangular

Question 14

14. If B is additive inverse of A then

Question 15

15.

Question 16

16. 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 17

17.

Answer

Identity matrix

Answer

Scairar matrix

Answer

Odd matrix

Answer

Even matrix

Question 18

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

Answer

Periodic matrix

Answer

Nilpotent matrix

Answer

Symmetric matrix

Answer

Idempotent matrix

Question 19

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

Answer

Inconsistent

Answer

Consistent

Answer

None of these

Question 20

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

Question 21

21. (ABC)’ =

Answer

C’B’A’

Question 22

22. (AB)t = ?

Question 23

23. An equation of the form ax + by = k is homogeneous linear equation when:

Answer

a = -0, a ≠ 0

Answer

a ≠ 0, b ≠ 0, k = 0

Answer

a = 0, b ≠ 0

Answer

b = 0, a = 0

Question 24

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

Question 25

25.

Answer

a = 3, b = 2

Answer

a = 2, b = 3

Answer

a = 2, b = 2

Answer

a = 3, b = 3

Question 26

26. Trivial solution of homogeneous linear equation is

Question 27

27.

Question 28

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

Answer

Scalar matrix

Answer

Hermitian matrix

Question 29

29.

Question 30

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

Answer

a, b and c

Question 31

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

Answer

None of these

Question 32

32. The transpose of a row matrix is a

Answer

Diagonal matrix

Answer

Zero matrix

Answer

Scalar matrix

Answer

Column matrix

Question 33

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

Answer

A¯¹B¯¹

Answer

B¯¹A¯¹

Question 34

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

Question 35

35.

Answer

a₁₁, a₁₂, a₁₃

Answer

a₂₁, a₂₂, a₂₃

Answer

a₁₁, a₂₁

Answer

None of these

Question 36

36.

Answer

Non – diagonal matrix

Answer

Zero matrix

Answer

Identity matrix

Answer

Row matrix

Question 37

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

Question 38

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

Question 39

39. The additive inverse of a matrix A is

Question 40

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

Answer

None of these

Question 41

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

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

Answer

Cofactor of the matrix

Answer

Reduced echlon form

Answer

Conjugate of the matrix

Answer

Rank of a matrix

Question 44

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

Answer

Aij = 0 for all i < j

Question 45

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

Question 46

46. [0 0 0] is

Answer

Scalar matrix

Answer

Diagonal matrix

Answer

Null matrix

Answer

Identity matrix

Question 47

47.

Answer

None of these

Question 48

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

Answer

Diagonal matrix

Question 49

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

Question 50

50.

Question 51

51. Two matrix A and B can be added if

Answer

Both have same order

Answer

Both are rectangular

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 52

52.

Question 53

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

Answer

Skew-symmetric

Answer

None of the above

Question 54

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

Question 55

55.

Question 56

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

Answer

All are true

Answer

(A¹) ≠ A

Answer

A + B ≠ B + A

Question 57

57.

Answer

Skew-hermitian

Answer

Skew – symmetric

Question 58

58.

Question 59

59.

Answer

II & III only

Question 60

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

Question 61

61.

Question 62

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

Answer

Both a and b

Answer

The secondary diagonal

Answer

The principal diagonal

Answer

None of these

Question 63

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

Question 64

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

Answer

Identity matrix

Answer

Rectangular matrix

Answer

Square matrix

Answer

Scalar matrix

Answer 92

Scalar matrix

Answer 93

Identity matrix

Answer 94

None of these

Answer 95

Diagonal matrix

Answer 96

Row matrix

Answer 97

Scalar matrix

Answer 98

Diagonal matrix

Answer 99

Column matrix

Answer 100

Diagonal matrix

Answer 101

Symmetric matrix

Answer 102

None of these

Answer 103

Hermition matrix

Answer 104

Multiplication of a column of a by any nonzero scalar

Answer 105

Interchange of any two columns of A

Answer 106

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

Answer 107

Interchange of any two rows of A

Answer 108

Singular matrix

Answer 109

Non- singular matrix

Answer 110

Zero matrix

Answer 111

None of these

Answer 112

System has one solution

Answer 113

System has no solution

Answer 114

None of these

Answer 115

System has two solutions

Answer 116

aij = 0 for all i > j

Answer 117

Non-symmetric

Answer 118

Square matrix

Answer 119

Rectangular matrix

Answer 120

Scalar matrix

Answer 121

Diagonal matrix

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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