Mathematics Matrices and Determinants Online Test

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Question 1

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

Answer

a, b and c

Question 2

2.

Question 3

3. 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 4

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

Answer

Inconsistent

Answer

None of these

Answer

Consistent

Question 5

5.

Question 6

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

Answer

(A¹) ≠ A

Answer

A + B ≠ B + A

Answer

All are true

Question 7

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

Answer

Non-symmetric

Question 8

8. For trival solution |A| is:

Question 9

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

Answer

Identity matrix

Answer

Square matrix

Answer

Rectangular matrix

Answer

Scalar matrix

Question 10

10. Minimum number of equation for any system of equations

Answer

None of these

Question 11

11. (AB)t = ?

Question 12

12.

Answer

Column matrix

Answer

Diagonal matrix

Answer

Zero matrix

Answer

Scalar matrix

Question 13

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

Question 14

14.

Question 15

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

Question 16

16. 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

Symmetric matrix

Answer

Hermition matrix

Question 17

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

Question 18

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

Answer

Diagonal matrix

Question 19

19. If B is additive inverse of A then

Question 20

20. Two matrices A and B are equal if

Answer

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

Answer

Both have same order

Answer

Both are rectangular

Answer

Both have same order and equal corresponding elements

Question 21

21.

Question 22

22.

Question 23

23. 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 24

24.

Answer

II & III only

Question 25

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

Answer

A¯¹B¯¹

Answer

B¯¹A¯¹

Question 26

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

Question 27

27. [-1, 4 7 2] is a

Answer

Diagonal matrix

Answer

Column matrix

Answer

Row matrix

Answer

Scalar matrix

Question 28

28.

Then order of matrix A = ?

Question 29

29. The transpose of a row matrix is a

Answer

Scalar matrix

Answer

Column matrix

Answer

Diagonal matrix

Answer

Zero matrix

Question 30

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

Question 31

31.

Question 32

32. 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 33

33. (CD)ᵗ = ?

Question 34

34. Equation having a common solution are called

Answer

Homogeneous equations

Answer

Simultaneous equation

Answer

None of these

Answer

Linear equations

Question 35

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

Question 36

36. The additive inverse of a matrix A is

Question 37

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

Answer

None of these

Answer

They are not equal

Answer

Each is equal to A

Answer

They are equal

Question 38

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

Answer

Conjugate of the matrix

Answer

Rank of a matrix

Answer

Cofactor of the matrix

Answer

Reduced echlon form

Question 39

39. 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 40

40. 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 41

41.

Answer

Identity matrix

Answer

Zero matrix

Answer

Non – diagonal matrix

Answer

Row matrix

Question 42

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

Answer

aij = 0 for all i > j

Question 43

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

Answer

Hermitian matrix

Answer

Scalar matrix

Question 44

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

Question 45

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

Answer

Singular matrix

Answer

Non- singular matrix

Answer

Zero matrix

Question 46

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

Question 47

47.

Answer

a₁₁, a₂₁

Answer

a₂₁, a₂₂, a₂₃

Answer

None of these

Answer

a₁₁, a₁₂, a₁₃

Question 48

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

Answer

Symmetric matrix

Answer

Nilpotent matrix

Answer

Periodic matrix

Answer

Idempotent matrix

Question 49

49. Trival solution of homogeneous linear equation is:

Answer

a, b and c

Question 50

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

Answer

None of these

Question 51

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

Question 52

52.

Answer

Identity matrix

Answer

Scairar matrix

Answer

Odd matrix

Answer

Even matrix

Question 53

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

Question 54

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

Question 55

55. Two matrix A and B can be added if

Answer

Both are rectangular

Answer

Both have same order

Answer

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

Answer

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

Question 56

56. The transpose of a square matrix is a

Answer

Diagonal matrix

Answer

Rectangular matrix

Answer

Scalar matrix

Answer

Square matrix

Question 57

57. (ABC)’ =

Answer

C’B’A’

Question 58

58.

Answer

None of these

Question 59

59.

Answer

Diagonal matrix

Answer

Identity matrix

Answer

None of these

Answer

Scalar matrix

Question 60

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

Answer

None of the above

Answer

Skew-symmetric

Question 61

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

Answer

Aij = 0 for all i < j

Question 62

62.

Answer

a = 2, b = 2

Answer

a = 3, b = 2

Answer

a = 3, b = 3

Answer

a = 2, b = 3

Question 63

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

Question 64

64. 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

Answer 105

System has one solution

Answer 106

None of these

Answer 107

System has two solutions

Answer 108

System has no solution

Answer 109

Skew-hermitian

Answer 110

Skew – symmetric

Answer 111

Both a and b

Answer 112

The principal diagonal

Answer 113

The secondary diagonal

Answer 114

None of these

Answer 115

None of these

Answer 116

1/|A|adj A

Answer 117

None of these

Answer 118

Identity matrix

Answer 119

Scalar matrix

Answer 120

Diagonal matrix

Answer 121

Null 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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