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

For non-trival solution |A| is

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

• 
  A
• 
  B
• 
  C
• 
  D

Which of the following is an identity matrix?

• 
  A
• 
  B
• 
  C
• none of these 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

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

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

• 1 A
• -1 B
• 0 C
• I D

• 
  A
• 
  B
• 
  C
• 
  D

A matrix with a single column is called

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

For trival solution |A| is

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

• 0 A
• 1 B
• -2 C
• 10 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

Trival solution of homogeneous linear equation is

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

The matrix A is Hermitian when (A)' =

• A A
• -A B
• A C
• A' 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

Minor of an element a_ijis denoted by

• M_ij A
• A_ij B
• |A| C
• None of these 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

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

• 0 A
• 1 B
• 2 C
• 3 D

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

• Null matrix A
• Triangular matrix B
• Unit matrix C
• Rectangular matrix D

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

• a²b²c² A
• 4a²b²c² B
• 4abc C
• None D

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

A matrix in which the number of rows is not equal to the number of columns is called a

• Diagonal matrix A
• Rectangular matrix B
• Square matrix C
• Scalar matrix D

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

• BA A
• A2 B
• AB C
• B2 D

Every identity matrix is

• Row-vector A
• Scalar B
• Column-vector C
• All D

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

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