Mathematics 4

Mathematics 

Q-1 If A is a rectangular matrix of order 3 × 4, then rank of a matrix is
(a) Less than equal to 3
(b) > 3
(c) 4
(d) None

Q-2 If characteristics eq. of a matrix of order 3 × 3 is cubic and it have different three root, then the minimal eq. will be of degree.
(a) 2
(b) 3
(c) 4
(d) 1

Q-3 In A3 – 7I = 0, Here we use I with 7, what is the reason behind it.
(a) To make it matrix
(b) To make it equal to A2
(c) To make it equal to A3
(d) None

Q-4 If in a Square Matrix, a row is zero, then it is
(a) Singular matrix
(b) Non singular matrix
(c) Hermition
(d) None

Q-5 If a matrix of order 3 have three non zero row, then ranks of A is
(a) 2
(b) 3
(c) 4
(d) 9

Q-6 What is the condition for the matrix to be Involuntary ?
(a) A3 = I
(b) A2 = I
(c) A = I
(d) None

Q-7 For upper triangular matrix
(a)aij = 0, i = j
(b) aij, i>j
(c) aij = 0, i no. of variable
(c) a and b
(d) None

Q-20 2x + 6y = 0 have
(a) Unique solution
(b) Infinite many solution
(c) No solution
(d) None

Q-21 If A2 = A, then it is
(a) Idempotent matrix
(b) Nilpotent matrix
(c) Involuntary matrix
(d) None

Q-22 (A + B)1 =?
(a) A1 – B1
(b) B1 – A1
(c) A1 + B1
(d) (B1)1

Q-23 If 2, 3, 4 are eigen value of A, then eigen value of A2 is
(a) (4, 9, 6)
(b) 4, 9, 16
(c) 5, 9, 16
(d) None

Q-24 If the upper triangular matrix have diagonal elements 2, 4, 8 then eigen value of this upper triangular matrix is
(a) 2, 4, 8
(b) 2, 4, 6
(c) 7, 5, 6
(d) 9, 10, 4

Q-25 If A is matrix of order 5 then its rank is
(a) 4
(b) 5
(c) 9
(d) 6

Answers

1(a) Less than equal to 3
2(b) 3
3(a) To make it matrix
4(a) Singular matrix
5(b) 3
6(b) A2 = I
7(b) aij, i > j
8(b) Characteristic eq.
9(c) 2
10(b) 3
11(a) 4
12(b) No
13(c) A1
14(a) Symmetric
15(b) Trivial Solution is x = y = z = 0
16(a) 4
17(b) Skew-Hermition
18(a) 4
19(a) Rank of A < no. of variable
20(b) Infinite many solution
21(a) Idempotent matrix
22(c) A1 + B1
23(b) 4, 9, 16
24(a) 2, 4, 8
25(c) 9

Reason

2 If roots are different then degree of characteristics eq. & minimal eq. is same
4 If any row of matrix is zero, then its A = 0, therefore it is singular matrix
11 For this A ¹ 0
Rank of A = 4
20 For 2x + 6y = 0 but y = K
2x + 6K = 0
2x = –6k , x = – 3k
x = – 3k, y = k,
k have so many value