ECAT Pre Engineering MCQ Test With Answer for Chapter 5 Mathematics

• A^- A
• A^t B
• -A C
• A 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

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

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

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

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

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

• K/6 A
• 2K B
• 3K C
• 6K 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

• 
  A
• 
  B
• 
  C
• 
  D

The transport of a square matrix is a

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

• 
  A
• 
  B
• 
  C
• 
  D

The square matrix A is skew-symmetric when At =

• -B A
• -C B
• -A C
• -D 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

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

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

If A is singular then |A| = ______

• 1 A
• 0 B
• 2 C
• None of these D

• -3 A
• -7 B
• 1 C
• 0 D

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

A matrix in which the number of rows is not equal to the number of columns is called a

• Diagonal matrix A
• Rectangular matrix B
• Square matrix C
• Scalar matrix D

• 1 A
• 0 B
• -1 C
• 2 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

If A is a non singular matrix then A^-1= ______

• 
  A
• 
  B
• 
  C
• 
  D

• 
  A
• 
  B
• 
  C
• 
  D

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

• 
  A
• 
  B
• 
  C
• 
  D

• 
  A
• 
  B
• 
  C
• 
  D