ECAT Pre Engineering Mathematic MCQ Test With Answer for Chapter 5 (Matrices and Determinants)

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

For trival solution |A| is

• A A
• |A| = 0 B
• A = 0 C
• |A|≠ 0 D

Matrix multiplication is

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

An equation of the form ax + by = k is homogeneous linear equation when

• b = 0, a = 0 A
• a = 0,b ≠ 0 B
• b = -0,a≠ 0 C
• a≠ 0,b≠ 0, k = 0 D

• A A
• -A B
• A^t C
• A^- 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

System of linear equation is inconsistent if

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

If A = [a_ij] 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
• 
  B
• 
  C
• 
  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

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 non-homogeneous linear system AX = B has no solution if

• |A| = 0 A
• |A|≠ 0 B
• Rank (a) = no of variables C
• Rank > no of variables D

• An upper triangular matrix A
• A lower triangular matrix B
• A diagonal matrix C
• A null matrix 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

• 
  A
• 
  B
• 
  C
• 
  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

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

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

• Scalar matrix A
• Identity matrix B
• Null matrix C
• Symmetric matrix D

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

• 
  A
• 
  B
• 
  C
• 
  D

• 
  A
• 
  B
• 
  C
• 
  D

• K/6 A
• 2K B
• 3K C
• 6K D

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

• 2 A
• 4 B
• 6 C
• 8 D

• 
  A
• 
  B
• 
  C
• 
  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

• a²b²c² A
• 4a²b²c² B
• 4abc C
• None D

The square matrix A is skew-symmetric when At =

• -B A
• -C B
• -A C
• -D D