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

The transpose of a column matrix is a ______

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

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

• 5 A
• 
  B
• -5 C
• none D

• Symmetric A
• Skew-symmetric B
• Hermitian C
• Skew hermitian D

• 
  A
• 
  B
• 
  C
• 
  D

• 
  A
• 
  B
• 
  C
• 
  D

• 
  A
• 
  B
• 
  C
• all are correct D

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

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

The square matrix A is skew-symmetric when At=

• -B A
• -C B
• -A C
• -D 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

• 
  A
• 
  B
• 
  C
• 
  D

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

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

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

• 
  A
• 
  B
• 
  C
• 
  D

Rank of matrix [1 3 5 0] is

• 1 A
• 3 B
• 2 C
• 4 D

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

• 
  A
• 
  B
• 
  C
• 
  D

If the matrices A and B have the order 1 x 10 and 10 x 1 then order of AB is

• 1 x 1 A
• 1 x 10 B
• 10 x 10 C
• 10 x 1 D

Every identity matrix is

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

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

• At Bt A
• AB B
• -AB C
• BA D

• 
  A
• 
  B
• 
  C
• 
  D

Minor of an element a_ijis denoted by

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

The transport of a square matrix is a

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