ECAT Pre Engineering MCQ Test With Answer for Chapter 5 Mathematics

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

The transpose of a row matrix is a ______

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

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

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

• (2x4) A
• (2x7) B
• (2x3) C
• (7x2) D

• 
  A
• 
  B
• 
  C
• 
  D

The matrix A = [aij]mxn with m≠n is

• Rectangular A
• Symmetric B
• Square C
• None 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

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

• 2s² A
• 2s³ B
• s³ C
• 3s³ D

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

Let A is a 3 x 3 matrix and B is its adjoint matrix. If |B| = 64, then |A| =

• 
  A
• 
  B
• 
  C
• 
  D

• Orthogonal A
• Involutary B
• Idempotent C
• Nilpotent D

• 
  A
• 
  B
• 
  C
• 
  D

• I3 A
• rI3 B
• r C
• none D

• 0 A
• abc B
• 1/abc C
• None of these D

• 5 A
• 
  B
• -5 C
• none 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 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

Trival solution of homogeneous linear equation is

• (0, 0, 0) A
• (1, 2, 3) B
• (1, 3, 5) C
• a, b and c D

• 
  A
• 
  B
• 
  C
• 
  D

The matrix A is Hermitian when (A)' =

• A A
• -A B
• A C
• A' 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 with a single row is called a

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

• 2 x 2 A
• 2 x 3 B
• 3 x 2 C
• 3 x 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

System of linear equations is inconsistent if

• System has no solution A
• System has one solution B
• System has two solution C
• None of above D

A square matrix A = [aij] is upper triangular when

• cij = 0 A
• bij = 0 B
• aij = 0 for all i > j C
• dij = 0 D