ECAT Pre Engineering MCQ Test With Answer for Chapter 5 Mathematics

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

If A is any matrix then its additive inverse is

• A A
• A^-1 B
• A^t C
• -A D

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

• A2 A
• A3 B
• A C
• None of above D

• 
  A
• 
  B
• 
  C
• 
  D

• 3, -3, 11 A
• 3, 3, 11 B
• -3, 3, -11 C
• -3, -3, 11 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
• 
  B
• 
  C
• 
  D

Let A be a square matrix. Then, 1/2 (A-A') is

• Skew-symmetric A
• Symmetric B
• Null C
• None of the above D

If A and B are skew-symmetric then (AB)t is

• At Bt A
• AB B
• -AB C
• BA D

Minor of an element a_ijis denoted by

• M_ij A
• A_ij B
• |A| C
• None of these D

If A and B are two matrices such that AB = B and BA = A then A2 + B2 =

• 2 AB A
• 2 BA B
• A + B C
• AB D

• 2s² A
• 2s³ B
• s³ C
• 3s³ 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

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

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

• Orthogonal A
• Involutary B
• Idempotent C
• Nilpotent 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

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

• 16 A
• 256 B
• 64 C
• 1024 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

• 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

Every identity matrix is

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

Which of the following is an identity matrix?

• 
  A
• 
  B
• 
  C
• none of these D

• k3 A
• 0 B
• 3k C
• k6 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

If A is skew Hermitian Matrix then which of the following is not skew Hermitian matrix

• A2 A
• A5 B
• A3 C
• A7 D

• 
  A
• 
  B
• 
  C
• 
  D

For non-trival solution |A| is

• non zero A
• A = 0 B
• |A| = 0 C
• At = 0 D

A diagonal matrix is always

• Identity A
• Triangular B
• Scalar C
• Non-singular D

The matrix A = [aij]mxn with m≠n is

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