ECAT Pre Engineering MCQ Test With Answer for Chapter 5 Mathematics

Matrix multiplication is

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

Rank of matrix [1 3 5 0] is

• 1 A
• 3 B
• 2 C
• 4 D

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

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

• 
  A
• 
  B
• 
  C
• 
  D

Matrices are represented by

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

The square matrix A is skew-symmetric when At=

• -B A
• -C B
• -A C
• -D D

• 4A - 3I A
• 3A - 4I B
• A - I C
• None of these D

Every identity matrix is

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

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

For non-trival solution |A| is

• A = 0 A
• A^t= 0 B
• |A| = 0 C
• None of these D

• 0 A
• 1 B
• 2 C
• 4 D

For any positive integer n

• ABn = Bn A ⇔ AB = BA A
• ABn = Bn A⇔ A,B are square matrices and AB = BA B
• ABn = BnA⇔ A + B C
• ABn = BnA ⇔ A and B are square matries 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 upper triangular when

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

• 
  A
• 
  B
• 
  C
• 
  D

• 
  A
• 
  B
• 
  C
• all are correct D

• 
  A
• 
  B
• 
  C
• all D

• 
  A
• 
  B
• 
  C
• 
  D

• 5 A
• 
  B
• -5 C
• none D

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

• 
  A
• 
  B
• 
  C
• 
  D

In order of A is m x n and order of B is n x p then order of AB is

• m x m A
• n x n B
• m x p C
• p x m D

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

• k3 A
• 0 B
• 3k C
• k6 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(α) - A(β) A
• A(α) + A(β) B
• A(α-β) C
• A(α+β) 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

Trival solution of homogeneous linear equation is

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

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