ECAT Pre Engineering Mathematic MCQ Test With Answer for Chapter 5 (Matrices and Determinants)

For trival solution |A| is

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

• 2 A
• 4 B
• 6 C
• 8 D

Let A be a square matrix. Then, 1/2 (A-A') is

• Skew-symmetric A
• Symmetric B
• Null C
• None of the above D

The matrix A is Hermitian when (A)' =

• A A
• -A B
• A C
• A' D

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

• 
  A
• 
  B
• 
  C
• all 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

• I3 A
• rI3 B
• r C
• none D

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

• 
  A
• 
  B
• 
  C
• 
  D

• 0 A
• Independent of a B
• Independent of b C
• Independent of c D

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

• 
  A
• 
  B
• 
  C
• 
  D

If order of A is m x n, then order of A^tis

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

The square matrix A is skew-symmetric when At=

• -B A
• -C B
• -A C
• -D D

• 
  A
• 
  B
• 
  C
• 
  D

Matrix multiplication is

• Commutative A
• Not commutative B
• Not associative C
• Not distributive D

For trival solution |A| is

• A A
• |A| = 0 B
• A = 0 C
• |A|≠ 0 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

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

• -a -b -c A
• 1 B
• 0 C
• -1 D

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

(ABC)' =

• CBA' A
• CBA B
• C'B'A C
• C'B'A' D

A matrix with a single column is called

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

Rank of matrix [1 3 5 0] is

• 1 A
• 3 B
• 2 C
• 4 D

• Identity matrix A
• Diagonal matrix B
• Null matrix C
• Hermitian matrix D

• 
  A
• 
  B
• 
  C
• 
  D

Two matrices A and B are conformable for the product AB if

• Both A and B are square A
• Both A and B are symmetric B
• Number of rows of A = number of columns of B C
• Number of columns of A = number of rows of B 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

• 0 A
• 1 B
• -2 C
• 10 D

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