ECAT Pre Engineering MCQ Test With Answer for Chapter 5 Mathematics

If for the matrix A,A5 = 1,then A-1=

• A2 A
• A3 B
• A C
• None of above D

If for the matrix A, A⁵= I, then A^-1=

• A² A
• A³ B
• A 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

Matrices A = [aij] 2 x 3 and B =[bij] 3 x 2 are suitable for

• BA A
• A² B
• AB C
• B² D

• 
  A
• 
  B
• 
  C
• 
  D

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

• -a -b -c A
• 1 B
• 0 C
• -1 D

The additive inverse of a matrix A is

• 
  A
• 
  B
• 
  C
• None of these D

If there are m rows and n columns in a matrix then its order is

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

• (2x+a+b+c) A
• (a+b+c) B
• (a+b+c+x) C
• 0 D

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

• 
  A
• 
  B
• 
  C
• 
  D

• 5 A
• 15 B
• 10 C
• 20 D

If A is a non-singular matrix then adj A is

• Non-singular A
• Symmetric B
• Singular C
• Non defined D

• 5 A
• 
  B
• -5 C
• none 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

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

The square matrix A is skew-symmetric when At =

• -B A
• -C B
• -A C
• -D D

If A is singular then |A| = ______

• 1 A
• 0 B
• 2 C
• None of these D

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

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

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

The matrix A = [aij]mxn with m ≠n is always

• Symmetric A
• Hermition B
• Skew-symmetric C
• None D

• 
  A
• 
  B
• 
  C
• 
  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

• 
  A
• 
  B
• 
  C
• 
  D

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

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

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