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

If there are m rows and n columns in a matrix then its order is

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

If the matrices A and B are conformable for multiplication then (AB)^t= ______

• AB A
• A^tB^t B
• B^tA^t C
• A^tB D

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

A and B be two square matrices and if their inverse exist, the (AB)^-1=

• A^-1B^-1 A
• AB^-1 B
• A^-1B C
• B^-1A^-1 D

Which of the following is an identity matrix?

• 
  A
• 
  B
• 
  C
• none of these D

A matrix in which the number of rows is equal to the number of columns is called a

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

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

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

Minor of an element a_ijis denoted by

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

• 0 A
• 1 B
• -A C
• -1 D

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

• 0 A
• 1 B
• 2 C
• 3 D

Which of the following is skew symmetric matrix

• 
  A
• 
  B
• 
  C
• 
  D

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

• 
  A
• 
  B
• 
  C
• 
  D

The transpose of a zero matrix is a ______

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

If A is a non-singular matrix then adj A is

• Non-singular A
• Symmetric B
• Singular C
• Non defined 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

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

• 
  A
• 
  B
• 
  C
• 
  D

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

The matrix A = [aij]1xn is a

• Vector A
• Rectangular matrix B
• Column vector C
• Square matrix D

If A is any matrix then its additive inverse is

• A A
• A^-1 B
• A^t C
• -A D

• A A
• -A B
• A^t C
• A^- D

• 
  A
• 
  B
• 
  C
• 
  D