ECAT Pre General Science MCQ Test With Answer for Mathematics Chapter 5

• 1 A
• -1 B
• 0 C
• I D

For non-trival solution |A| is

• A = 0 A
• A^t= 0 B
• |A| = 0 C
• None of these D

• 3 x 1 A
• 1 x 3 B
• 3 x 3 C
• 1 x 1 D

• 
  A
• 
  B
• 
  C
• 
  D

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 A
• Symmetric B
• Null C
• Diagonal D

For a square matrix A, if A = A^t, then A is called

• matrix A
• Transpose B
• Symmetric C
• Non-symmetric D

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 A
• Symmetric B
• Null C
• Diagonal D

• 
  A
• 
  B
• 
  C
• all are correct D

• 0 A
• 1 B
• 2 C
• 4 D

For trival solution |A| is

• A A
• |A| is non zero B
• A = 0 C
• None of these D

If the trace of matrix A is 5, then the trace of the matrix 3A is

• 3/5 A
• 5/3 B
• 8 C
• 15 D

If A is a non singular matrix then A^-1= ______

• 
  A
• 
  B
• 
  C
• 
  D

For any positive integer n

• ABn = Bn A ⇔ AB = BA A
• ABn = Bn A⇔ A,B are square matrices and AB = BA B
• ABn = BnA⇔ A + B C
• ABn = BnA ⇔ A and B are square matries D

If A is any matrix then its additive inverse is

• A A
• A^-1 B
• A^t C
• -A D

Trival solution of homogeneous linear equation is

• (0, 0, 0) A
• (1, 2, 3) B
• (1, 3, 5) C
• a.b and c D

• 
  A
• 
  B
• 
  C
• 
  D

• 16 A
• 256 B
• 64 C
• 1024 D

We also the system of non-homogeneous linear equations by

• a and b A
• b and c B
• c and a C
• a, b and c D

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

• m x m A
• m x n B
• n x n C
• n x m D

The transpose of a column matrix is a ______

• Zero matrix A
• Diagonal matrix B
• Column matrix C
• Row matrix D

The number of non zero rows in echelon form of a matrix is called

• Order of matrix A
• Rank of matrix B
• Row operation C
• None of these D

• 
  A
• 
  B
• 
  C
• 
  D

• (2x+a+b+c) A
• (a+b+c) B
• (a+b+c+x) C
• 0 D

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

• aij = 0 for all i < j A
• bij = 0 B
• cij = 0 C
• dij =0 D

• Diagonal matrix A
• Scalar matrix B
• Triangular matrix C
• Identity matrix D

• 2 x 2 A
• 2 x 3 B
• 3 x 2 C
• 3 x 3 D

• I A
• |A| B
• |A| I C
• None of these D

(ABC)' =

• CBA' A
• CBA B
• C'B'A C
• C'B'A' D

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

• 
  A
• 
  B
• 
  C
• 
  D

• 
  A
• 
  B
• 
  C
• 
  D