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

The matrix A = [aij]mxn with m≠n is

• Rectangular A
• Symmetric B
• Square C
• None D

• 0 A
• 1 B
• -A C
• -1 D

For trival solution |A| is

• A A
• |A| = 0 B
• A = 0 C
• |A|≠ 0 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

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

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

A and B be two square matrices and if their inverse exist the (AB)-1 =

• A-1 B-1 A
• AB-1 B
• A-1B C
• B-1A-1 D

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

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

• I A
• |A| B
• |A| I C
• None of these D

• 
  A
• 
  B
• 
  C
• 
  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 A
• -A B
• A^t C
• A^- D

For trival solution |A| is

• A A
• |A| is non zero B
• A = 0 C
• None of these D

• 
  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

Cofactor of an element aij denoted by Aij is

• (-2)i+j A
• Mij B
• (-1)i+j Mij C
• None of above D

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

If the matrices A and B are conformable for multiplication then (AB)^t= ______

• AB A
• A^tB^t B
• B^tA^t C
• A^tB 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

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

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

• 1 A
• 0 B
• 3 C
• -1 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

• Null matrix A
• Triangular matrix B
• Unit matrix C
• Rectangular matrix D

• 5 A
• 15 B
• 10 C
• 20 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