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

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

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

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

• 
  A
• 
  B
• 
  C
• 
  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

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

• A² A
• A³ B
• A C
• None of above D

• 
  A
• 
  B
• 
  C
• all D

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

• b = 0, a = 0 A
• a = 0,b ≠ 0 B
• b = -0,a≠ 0 C
• a≠ 0,b≠ 0, k = 0 D

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

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

The transpose of a row matrix is a ______

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

• (2x4) A
• (2x7) B
• (2x3) C
• (7x2) D

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

• 3K A
• K2 B
• K3 C
• K D

• 2 A
• 4 B
• 6 C
• 8 D

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

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

If A = [aij]mxpand B =[aij]pxnthen order of BA is

• m x n A
• p x n B
• n x m C
• None of these D

• Symmetric A
• Skew-symmetric B
• Hermitian C
• Skew hermitian D

• 16 A
• 256 B
• 64 C
• 1024 D

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

If A is any matrix then its additive inverse is

• A A
• A^-1 B
• A^t C
• -A D

A square matrix all of whose elements except the main diagonal are zeros is called a

• Null matrix A
• Singular matrix B
• Symmetric matrix C
• Diagonal matrix D

If A is singular then |A| = ______

• 1 A
• 0 B
• 2 C
• None of these D

Matrices A = [aij] 2 x 3 and B = [bij] 3 x 2 are suitable for

• BA A
• A2 B
• AB C
• B2 D

• 
  A
• 
  B
• 
  C
• 
  D

• A^- A
• A^t B
• -A C
• A D

For trival solution |A| is

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