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

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

We also the system of non-homogeneous linear equations by

• a and b A
• b and c B
• c and a C
• a, b and c 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

For non-trival solution |A| is

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

The transpose of a row matrix is a ______

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

The transpose of a column matrix is a ______

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

For non-trival solution |A| is

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

• 1 A
• -1 B
• 0 C
• I D

A square matrix A = [aij] is upper triangular when

• cij = 0 A
• bij = 0 B
• aij = 0 for all i > j C
• dij = 0 D

If A is a non singular matrix then A^-1= ______

• 
  A
• 
  B
• 
  C
• 
  D

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

• A2 A
• A3 B
• A C
• None of above 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

• I A
• 14 I B
• 0 C
• None of these D

• I A
• |A| B
• |A| I 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

• 
  A
• 
  B
• 
  C
• all are correct D

• 
  A
• 
  B
• 
  C
• 
  D

• 0 A
• 1 B
• -2 C
• 10 D

• 2s² A
• 2s³ B
• s³ C
• 3s³ D

(ABC)' =

• CBA' A
• CBA B
• C' B' A' C
• None of these D

• 
  A
• 
  B
• 
  C
• 
  D

• 4A - 3I A
• 3A - 4I B
• A - I C
• None of these D

• 
  A
• 
  B
• 
  C
• 
  D

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

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

• 1 A
• 0 B
• 3 C
• -1 D

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

• 
  A
• 
  B
• 
  C
• 
  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