ECAT Pre Engineering MCQ Test With Answer for Chapter 5 Mathematics

• 
  A
• 
  B
• 
  C
• all are correct D

• -a -b -c A
• 1 B
• 0 C
• -1 D

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

The transpose of a zero matrix is a ______

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

• I3 A
• rI3 B
• r C
• none D

For a square matrix A, if A = A^t, then A is called

• matrix A
• Transpose B
• Symmetric C
• Non-symmetric D

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

• 5 A
• 15 B
• 10 C
• 20 D

The transpose of a column matrix is a ______

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

• 
  A
• 
  B
• 
  C
• 
  D

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

Two matrices A and B are conformable for the product AB if

• Both A and B are square A
• Both A and B are symmetric B
• Number of rows of A = number of columns of B C
• Number of columns of A = number of rows of B D

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

• 0 A
• 1 B
• -A C
• -1 D

The matrix A = [aij]1xn is a

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

If there are m rows and n columns in a matrix then its order is

• m x n A
• m x m B
• n x n C
• n x m 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

Matrix multiplication is

• Commutative A
• Not commutative B
• Not associative C
• Not distributive D

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

• At Bt A
• AB B
• -AB C
• BA D

Matrices are represented by

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

• 
  A
• 
  B
• 
  C
• 
  D

• 
  A
• 
  B
• 
  C
• 
  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

Which of the following is an identity matrix?

• 
  A
• 
  B
• 
  C
• none of these D

The matrix A = [aij]mxn with m≠n is

• Rectangular A
• Symmetric B
• Square C
• None 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