ECAT Mathematics Chapter 5 Matrices and Detarminants Online Test With Answers

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ECAT Mathematics Chapter 5 Matrices and Detarminants Online Test

Sr. # Questions Answers Choice
1 9/4 4/9 1 None of these
2 2s<sup>2</sup> 2s<sup>3</sup> s<sup>3</sup> 3s<sup>3</sup>
3 K/6 2K 3K 6K
4 Let A is a 3 x 3 matrix and B is its adjoint matrix. If |B| = 64, then |A| =
5 0 Independent of a Independent of b Independent of c
6 0 abc 1/abc None of these
7
8 Orthogonal Involutary Idempotent Nilpotent
9 a = 4, b = 1 a = 1, b = -4 a = 0, b = 4 a = 2, b = 4
10
11 Symmetric Skew-symmetric Hermitian Skew hermitian
12 4A - 3I 3A - 4I A - I None of these
13 A(<span style="color: rgb(34, 34, 34); font-family: &quot;Times New Roman&quot;; font-size: 24px; text-align: center; background-color: rgb(255, 255, 224);"><i>α</i></span>) - A(<span style="color: rgb(34, 34, 34); font-family: &quot;Times New Roman&quot;; font-size: 24px; text-align: center; background-color: rgb(255, 255, 248);"><i>β</i></span>) A(<span style="font-family: &quot;Times New Roman&quot;; font-size: 24px; color: rgb(34, 34, 34); text-align: center; background-color: rgb(255, 255, 224);"><i>α</i></span>) + A(<span style="font-family: &quot;Times New Roman&quot;; font-size: 24px; color: rgb(34, 34, 34); text-align: center; background-color: rgb(255, 255, 248);"><i>β</i></span>) A(<i style="text-align: center;">α</i>-<i style="text-align: center;">β</i>) A(<i style="text-align: center;">α</i>+<i style="text-align: center;">β</i>)
14 6, -12, -18 -6, 4, 9 -6, -4, -9 -6, 12, 18
15 The order of the matrix A is 3 x 2 and that of B is 2 x 3. The order of the matrix BA is 3 x 3 3 x 2 2 x 5 5 x 2
16 0 1 2 4
17 If the trace of matrix A is 5, then the trace of the matrix 3A is 3/5 5/3 8 15
18 If for the matrix A, A5= I, then A-1= A<sup>2</sup> A<sup>3</sup> A None of above
19 I |A| |A| I None of these
20 For a square matrix A, if A = At, then A is called matrix Transpose Symmetric Non-symmetric
21 If A = [aij] is (m x n) matrix, then transpose of A is of the order m x m m x n n x n n x m
22 We also the system of non-homogeneous linear equations by a and b b and c c and a a, b and c
23 Trival solution of homogeneous linear equation is (0, 0, 0) (1, 2, 3) (1, 3, 5) a, b and c
24 For non-trival solution |A| is A = 0 A<sup>t</sup>= 0 |A| = 0 None of these
25 For trival solution |A| is A |A| is non zero A = 0 None of these
26 System of linear equations is inconsistent if System has no solution System has one solution System has two solution None of above
27 An equation of the form ax + by = k is homogeneous linear equation when:
28
29 A -A A<sup>t</sup> A<sup>-</sup>
30 A<sup>-</sup> A<sup>t</sup> -A A
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