Mathematics Matrices and Determinants Online Test

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Question 1

1.

Question 2

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

Answer

The secondary diagonal

Answer

Both a and b

Answer

None of these

Answer

The principal diagonal

Question 3

3.

Question 4

4. Two matrices A and B are equal if

Answer

Both are rectangular

Answer

Both have same order and equal corresponding elements

Answer

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

Answer

Both have same order

Question 5

5. 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 6

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

Question 7

7. (ABC)’ =

Answer

C’B’A’

Question 8

8. Trivial solution of homogeneous linear equation is

Question 9

9.

Answer

Skew-hermitian

Answer

Skew – symmetric

Question 10

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

Answer

a = -0, a ≠ 0

Answer

a = 0, b ≠ 0

Answer

b = 0, a = 0

Answer

a ≠ 0, b ≠ 0, k = 0

Question 11

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

Answer

None of these

Question 12

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

Answer

Non- singular matrix

Answer

Singular matrix

Answer

Zero matrix

Question 13

13. 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 14

14. [-1, 4 7 2] is a

Answer

Column matrix

Answer

Diagonal matrix

Answer

Scalar matrix

Answer

Row matrix

Question 15

15.

Answer

a₁₁, a₁₂, a₁₃

Answer

None of these

Answer

a₂₁, a₂₂, a₂₃

Answer

a₁₁, a₂₁

Question 16

16.

Question 17

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

Question 18

18.

Question 19

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

Answer

Periodic matrix

Answer

Nilpotent matrix

Answer

Idempotent matrix

Answer

Symmetric matrix

Question 20

20. (AB)t = ?

Question 21

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

Answer

Aij = 0 for all i < j

Question 22

22. 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 23

23.

Answer

Zero matrix

Answer

Diagonal matrix

Answer

Scalar matrix

Answer

Column matrix

Question 24

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

Question 25

25.

Question 26

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

Answer

1/|A|adj A

Answer

None of these

Question 27

27. An elementary row operation on a matrix A is

Answer

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

Answer

Interchange of any two columns of A

Answer

Interchange of any two rows of A

Answer

Multiplication of a column of a by any nonzero scalar

Question 28

28. 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 29

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

Question 30

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

Question 31

31.

Question 32

32. Two matrix A and B can be added if

Answer

Both have same order

Answer

Both are rectangular

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 33

33.

Answer

Non – diagonal matrix

Answer

Row matrix

Answer

Identity matrix

Answer

Zero matrix

Question 34

34. Trival solution of homogeneous linear equation is:

Answer

a, b and c

Question 35

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

Answer

Skew-symmetric

Answer

None of the above

Question 36

36. For trival solution |A| is:

Question 37

37. The transpose of a square matrix is a

Answer

Diagonal matrix

Answer

Rectangular matrix

Answer

Square matrix

Answer

Scalar matrix

Question 38

38.

Answer

Identity matrix

Answer

Scairar matrix

Answer

Even matrix

Answer

Odd matrix

Question 39

39. Minimum number of equation for any system of equations

Answer

None of these

Question 40

40.

Question 41

41. The additive inverse of a matrix A is

Question 42

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

Question 43

43. The transpose of a row matrix is a

Answer

Column matrix

Answer

Scalar matrix

Answer

Zero matrix

Answer

Diagonal matrix

Question 44

44. 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 45

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

Answer

aij = 0 for all i > j

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 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 48

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

Answer

B¯¹A¯¹

Answer

A¯¹B¯¹

Question 49

49. System of linear equations is inconsistent if:

Answer

None of these

Answer

System has no solution

Answer

System has two solutions

Answer

System has one solution

Question 50

50.

Answer

a = 3, b = 2

Answer

a = 2, b = 2

Answer

a = 2, b = 3

Answer

a = 3, b = 3

Question 51

51. 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 52

52. [0 0 0] is

Answer

Diagonal matrix

Answer

Identity matrix

Answer

Null matrix

Answer

Scalar matrix

Question 53

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

Question 54

54.

Question 55

55.

Answer

None of these

Question 56

56.

Question 57

57.

Question 58

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

Answer

Cofactor of the matrix

Answer

Rank of a matrix

Answer

Conjugate of the matrix

Answer

Reduced echlon form

Question 59

59.

Then order of matrix A = ?

Question 60

60. (CD)ᵗ = ?

Question 61

61. 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 62

62. If B is additive inverse of A then

Question 63

63.

Question 64

64.

Answer

Scalar matrix

Answer

Diagonal matrix

Answer

None of these

Answer

Identity matrix

Answer 103

Scalar matrix

Answer 104

Hermitian matrix

Answer 105

Diagonal matrix

Answer 106

They are not equal

Answer 107

They are equal

Answer 108

None of these

Answer 109

Each is equal to A

Answer 110

II & III only

Answer 111

None of these

Answer 112

None of these

Answer 113

Simultaneous equation

Answer 114

Homogeneous equations

Answer 115

Linear equations

Answer 116

a, b and c

Answer 117

Non-symmetric

Answer 118

Rectangular matrix

Answer 119

Identity matrix

Answer 120

Square matrix

Answer 121

Scalar 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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