ECAT Pre Engineering MCQ Test With Answer for Chapter 5 Mathematics

Rank of matrix [1 3 5 0] is

• 1 A
• 3 B
• 2 C
• 4 D

The square matrix A is skew-symmetric when At=

• -B A
• -C B
• -A C
• -D D

For non-trival solution |A| is

• A = 0 A
• A^t= 0 B
• |A| = 0 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

Minor of an element a_ijis denoted by

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

• 0 A
• 1 B
• 2 C
• 4 D

• 
  A
• 
  B
• 
  C
• 
  D

Matrices are represented by

• Natural numbers A
• Real numbers B
• Small letters C
• Capital letters D

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

• BA A
• A² B
• AB C
• B² D

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

• 9/4 A
• 4/9 B
• 1 C
• None of these 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

• 3, -3, 11 A
• 3, 3, 11 B
• -3, 3, -11 C
• -3, -3, 11 D

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

• Identity matrix A
• Diagonal matrix B
• Null matrix C
• Hermitian matrix D

• 1 A
• 0 B
• -1 C
• 2 D

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

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

• a = 2, b = 3 A
• a = 3, b = 2 B
• a = 2, b = 1, 2 C
• a = 3, b = 3 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
• 
  B
• 
  C
• 
  D

We solve 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

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

The order of the matrix A is 3 x 5 and that of B is 2 x 3.The order of the matrix BA is

• 2 x 3 A
• 3 x 2 B
• 2 x 5 C
• 5 x 2 D

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

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

• I3 A
• rI3 B
• r C
• none D

A = [3] is a/an

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