Mathematics ECAT Pre Engineering Chapter 5 Matrices and Determinants Online Test With Answers

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Mathematics ECAT Pre Engineering Chapter 5 Matrices and Determinants Online Test

Sr. # Questions Answers Choice
1 Trival solution of homogeneous linear equation is (0, 0, 0) (1, 2, 3) (1, 3, 5) a.b and c
2 For non-trival solution |A| is non zero A = 0 |A| = 0 At = 0
3 For trival solution |A| is A |A| = 0 A = 0 |A|≠ 0
4 System of linear equation is inconsistent if System has no solution System has one solution System has two solution None of above
5 An equation of the form ax + by = k is homogeneous linear equation when b = 0, a = 0 a = 0,b ≠ 0 b = -0,a≠ 0 a≠ 0,b≠ 0, k = 0
6 The matrix A is Hermitian when (A)' = A -A A A'
7 The square matrix A is skew Hermitian when (A)'= A A' -A A
8 The square matrix A is skew-symmetric when At = -B -C -A -D
9 A square matrix A = [aij] is upper triangular when cij = 0 bij = 0 aij = 0 for all i > j dij = 0
10 A square matrix A = [aij] is lower triangular matrix when aij = 0 for all i<j bij = 0 cij = 0 dij = 0
11 Cofactor of an element aij denoted by Aij is (-2)i+j Mij (-1)i+j Mij None of above
12 Matrices A = [aij] 2 x 3 and B = [bij] 3 x 2 are suitable for BA A2 AB B2
13 A and B be two square matrices and if their inverse exist the (AB)-1 = A-1 B-1 AB-1 A-1B B-1A-1
14 If A and B are two matrices such that AB = B and BA = A then A2 + B2 = 2 AB 2 BA A + B AB
15 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
16 (ABC)' = CBA' CBA C'B'A C'B'A'
17 For any positive integer n ABn = Bn A ⇔ AB = BA ABn = Bn A⇔ A,B are square matrices and AB = BA ABn = BnA⇔ A + B ABn = BnA ⇔ A and B are square matries
18 A diagonal matrix is always Identity Triangular Scalar Non-singular
19 The matrix A = [aij]mxn with m ≠n is always Symmetric Hermition Skew-symmetric None
20 The matrix A = [aij]1xn is a Vector Rectangular matrix Column vector Square matrix
21 The matrix A = [aij]mxn with m≠n is Rectangular Symmetric Square None
22 If the matrices A and B have the order 1 x 10 and 10 x 1 then order of AB is 1 x 1 1 x 10 10 x 10 10 x 1
23 If A and B are skew-symmetric then (AB)t is At Bt AB -AB BA
24 Every identity matrix is Row-vector Scalar Column-vector All
25 A non-homogeneous linear system AX = B has no solution if |A| = 0 |A|≠ 0 Rank (a) = no of variables Rank > no of variables
26 If A is a non-singular matrix then adj A is Non-singular Symmetric Singular Non defined
27 Matrix multiplication is Commutative Not commutative Not associative Not distributive
28 If A = [aij]mxpand B =[aij]pxnthen order of BA is m x n p x n n x m None of these
29 A = [3] is a/an Square matrix Scalar matrix Diagonal matrix Identity matrix
30 all are correct
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