ECAT Pre Engineering MCQ Test With Answer for Chapter 5 Mathematics

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

The transport of a square matrix is a

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

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

If the trace of matrix A is 5, then the trace of the matrix 3A is

• 3/5 A
• 5/3 B
• 8 C
• 15 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

• An upper triangular matrix A
• A lower triangular matrix B
• A diagonal matrix C
• A null matrix D

• 
  A
• 
  B
• 
  C
• 
  D

• 
  A
• 
  B
• 
  C
• 
  D

A square matrix A for which A^t= -A is called a

• Column matrix A
• Symmetric matrix B
• Skew-symmetric matrix C
• Row matrix D

The transpose of a zero matrix is a ______

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

The transpose of a column matrix is a ______

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

Which of the following is skew symmetric matrix

• 
  A
• 
  B
• 
  C
• 
  D

• Singular A
• Non-singular B
• Adjoint C
• None of above D

• -a -b -c A
• 1 B
• 0 C
• -1 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

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

If A is any matrix then its additive inverse is

• A A
• A^-1 B
• A^t C
• -A D

For trival solution |A| is

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

• k3 A
• 0 B
• 3k C
• k6 D

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

If A is singular then |A| = ______

• 1 A
• 0 B
• 2 C
• None of these D

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

Every identity matrix is

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