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

A matrix with a single row is called a

• Column matrix A
• Row matrix B
• Null matrix C
• Identity matrix D

• 3, -3, 11 A
• 3, 3, 11 B
• -3, 3, -11 C
• -3, -3, 11 D

• 0 A
• 1 B
• 2 C
• 4 D

Rank of matrix [1 3 5 0] is

• 1 A
• 3 B
• 2 C
• 4 D

If for the matrix A, A⁵= I, then A^-1=

• A² A
• A³ B
• A C
• None of above D

• Orthogonal A
• Involutary B
• Idempotent C
• Nilpotent D

We solve 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

• a = 4, b = 1 A
• a = 1, b = -4 B
• a = 0, b = 4 C
• a = 2, b = 4 D

In order of A is m x n and order of B is n x p then order of AB is

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

If A and B are two matrices such that AB = B and BA =A, then A²+ B²=

• 2 AB A
• 2 BA B
• A + B C
• AB D

• 4A - 3I A
• 3A - 4I B
• A - I C
• None of these 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

• 9/4 A
• 4/9 B
• 1 C
• None of these D

• A(α) - A(β) A
• A(α) + A(β) B
• A(α-β) C
• A(α+β) D

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

• 
  A
• 
  B
• 
  C
• 
  D

• I A
• 14 I B
• 0 C
• None of these D

• 
  A
• 
  B
• 
  C
• 
  D

• 
  A
• 
  B
• 
  C
• all D

The order of the matrix A is 3 x 5 and that of B is 2 x 3.The order of the matrix BA is

• 2 x 3 A
• 3 x 2 B
• 2 x 5 C
• 5 x 2 D

• 1 A
• 0 B
• -1 C
• 2 D

• 2 A
• 4 B
• 6 C
• 8 D

Let A is a 3 x 3 matrix and B is its adjoint matrix. If |B| = 64, then |A| =

• 
  A
• 
  B
• 
  C
• 
  D

• a = 2, b = 3 A
• a = 3, b = 2 B
• a = 2, b = 1, 2 C
• a = 3, b = 3 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

• 2s² A
• 2s³ B
• s³ C
• 3s³ D

• 1 A
• 0 B
• 3 C
• -1 D

• a = -1/2, b = -1 A
• a = 1, b = 2 B
• a = 2, b = 3 C
• None of above D

The matrix A = [aij]mxn with m ≠n is always

• Symmetric A
• Hermition B
• Skew-symmetric C
• None 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

The transport of a null matrix is

• Row matrix A
• Column matrix B
• Square matrix C
• Null matrix D