ECAT Pre General Science Mathematics Chapter 5 Matrics and Determinants Online Test With Answers

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ECAT Pre General Science Mathematics Chapter 5 Matrics and Determinants Online Test

Sr. # Questions Answers Choice
1 The square matrix A is skew-symmetric when At= -B -C -A -D
2 A square matrix A = [aij] is upper triangular when cij = 0 bij = 0 aij = 0 for all i > j dij = 0
3 A square matrix A = [aij] is lower triangular matrix when: aij = 0 for all i < j bij = 0 cij = 0 dij =0
4 Singular Non-singular Adjoint None of above
5 Matrices A = [aij] 2 x 3 and B =[bij] 3 x 2 are suitable for BA A<sup>2</sup> AB B<sup>2</sup>
6
7 a = -1/2, b = -1 a = 1, b = 2 a = 2, b = 3 None of above
8 x =0, y =4 x = -1, y = 2 x = 2, y = 3 x = 3, y = 4
9
10 A and B be two square matrices and if their inverse exist, the (AB)-1= A<sup>-1</sup>B<sup>-1</sup> AB<sup>-1</sup> A<sup>-1</sup>B B<sup>-1</sup>A<sup>-1</sup>
11 I 14 I 0 None of these
12 If A and B are two matrices such that AB = B and BA =A, then A2+ B2= 2 AB 2 BA A + B AB
13
14 3, -3, 11 3, 3, 11 -3, 3, -11 -3, -3, 11
15
16 a<sup>2</sup>b<sup>2</sup>c<sup>2</sup> 4a<sup>2</sup>b<sup>2</sup>c<sup>2</sup> 4abc None
17
18 1 -1 0 I
19 Let A be a square matrix. Then, 1/2 (A-A') is Skew-symmetric Symmetric Null None of the above
20 If A is a skew-symmetric matrix of order n and P, any square matrix of order n, prove that P' AP is Skew-symmetric Symmetric Null Diagonal
21 (ABC)' = CBA' CBA C' B' A' None of these
22 1 0 -1 2
23 1 0 3 -1
24 -3 -7 1 0
25 A<sup>2</sup>- 5A + 7I = 1 2A<sup>2</sup>- 3A + 7I = 0 A<sup>2</sup>- 5A + I = 0 A<sup>2</sup>- 5A + 7I = 0
26
27
28 a = 2, b = 3 a = 3, b = 2 a = 2, b = 1, 2 a = 3, b = 3
29 Which of the following is an identity matrix? none of these
30 0 1 -A -1
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