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

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

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

A matrix with a single row is called a

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

• 
  A
• 
  B
• 
  C
• 
  D

• I3 A
• rI3 B
• r C
• none D

If A = |aij| 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

For non-trival solution |A| is

• non zero A
• A = 0 B
• |A| = 0 C
• At = 0 D

• 
  A
• 
  B
• 
  C
• 
  D

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 A
• 3 x 2 B
• 2 x 5 C
• 5 x 2 D

• 6, -12, -18 A
• -6, 4, 9 B
• -6, -4, -9 C
• -6, 12, 18 D

• Scalar matrix A
• Identity matrix B
• Null matrix C
• Symmetric matrix D

The matrix A = [aij]mxn with m≠n is

• Rectangular A
• Symmetric B
• Square C
• None D

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

• 1 A
• -1 B
• 0 C
• I 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 square matrix A is skew-symmetric when At=

• -B A
• -C B
• -A C
• -D D

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

• 0 A
• abc B
• 1/abc C
• None of these D

Matrix multiplication is

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

• 0 A
• 1 B
• -2 C
• 10 D

The matrix A is Hermitian when (A)' =

• A A
• -A B
• A C
• A' D

• A^- A
• A^t B
• -A C
• A D

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

A diagonal matrix in which the diagonal elements are equal is called a

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

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

• 
  A
• 
  B
• 
  C
• 
  D

Cofactor of an element a_ijis defined by

• (-1)^i+j|A| A
• (-1)^i+jM_ij B
• (-1)^i+jM^-1 C
• None of these D

Cofactor of an element aij denoted by Aij is

• (-2)i+j A
• Mij B
• (-1)i+j Mij C
• None of above D

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

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