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

Which of the following is an identity matrix?

• 
  A
• 
  B
• 
  C
• none of these D

The transpose of a column matrix is a ______

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

• 5 A
• 15 B
• 10 C
• 20 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

• 0 A
• 1 B
• 2 C
• 4 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

• K/6 A
• 2K B
• 3K C
• 6K 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

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

• 
  A
• 
  B
• 
  C
• 
  D

• 1, 2, 3 A
• 1, 5, 9 B
• 2, 5, 8 C
• 3, 6, 9 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

• 0 A
• 1 B
• 2 C
• 3 D

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

The order of the matrix [1 2 3] is

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

• k3 A
• 0 B
• 3k C
• k6 D

• Hermitian matrix A
• Skew-hermitian matrix B
• Symmetric matrix C
• Identity matrix D

• 
  A
• 
  B
• 16 C
• None of these D

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

(ABC)' =

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

• 
  A
• 
  B
• 
  C
• 
  D

• 
  A
• 
  B
• 
  C
• 
  D

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

• BA A
• A2 B
• AB C
• B2 D

• A²- 5A + 7I = 1 A
• 2A²- 3A + 7I = 0 B
• A²- 5A + I = 0 C
• A²- 5A + 7I = 0 D

Cofactor of an element a_ijis defined by

• (-1)^i+j|A| A
• (-1)^i+jM_ij B
• (-1)^i+jM^-1 C
• None of these D

• 
  A
• 
  B
• 
  C
• 
  D