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

The transpose of a zero matrix is a ______

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

A matrix with a single row is called a

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

The transport of a square matrix is a

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

• a = 4, b = 1 A
• a = 1, b = -4 B
• a = 0, b = 4 C
• a = 2, b = 4 D

Minor of an element a_ijis denoted by

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

• 2s² A
• 2s³ B
• s³ C
• 3s³ 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

• x =0, y =4 A
• x = -1, y = 2 B
• x = 2, y = 3 C
• x = 3, y = 4 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

• -3 A
• -7 B
• 1 C
• 0 D

The matrix A is Hermitian when (A)' =

• A A
• -A B
• A C
• A' D

• 
  A
• 
  B
• 
  C
• 
  D

For non-trival solution |A| is

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

If A and B are skew-symmetric then (AB)t is

• At Bt A
• AB B
• -AB C
• BA D

The matrix A = [aij]1xn is a

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

• 5 A
• 15 B
• 10 C
• 20 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

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

If A = [a_ij] 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

• 0 A
• 1 B
• -A C
• -1 D

• 16 A
• 256 B
• 64 C
• 1024 D

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

• 1 A
• 0 B
• 3 C
• -1 D

The square matrix A is skew-symmetric when At=

• -B A
• -C B
• -A C
• -D D

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

• 
  A
• 
  B
• 
  C
• 
  D

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

• 
  A
• 
  B
• 
  C
• 
  D