ECAT Pre Engineering MCQ Test With Answer for Chapter 5 Mathematics

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

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

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

• 
  A
• 
  B
• 
  C
• 
  D

• -3 A
• -7 B
• 1 C
• 0 D

The transport of a null matrix is

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

The square matrix A is skew-symmetric when At=

• -B A
• -C B
• -A C
• -D D

• 
  A
• 
  B
• 
  C
• 
  D

Rank of matrix [1 3 5 0] is

• 1 A
• 3 B
• 2 C
• 4 D

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

The transpose of a zero matrix is a ______

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

• 1, 2, 3 A
• 1, 5, 9 B
• 2, 5, 8 C
• 3, 6, 9 D

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

• 
  A
• 
  B
• 
  C
• 
  D

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

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

Which of the following is skew symmetric matrix

• 
  A
• 
  B
• 
  C
• 
  D

• 0 A
• 1 B
• -A C
• -1 D

Matrices are represented by

• Natural numbers A
• Real numbers B
• Small letters C
• Capital letters 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

• 5 A
• 15 B
• 10 C
• 20 D

• I3 A
• rI3 B
• r C
• none D

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

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

• 
  A
• 
  B
• 
  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

• (2x4) A
• (2x7) B
• (2x3) C
• (7x2) D

• 
  A
• 
  B
• 
  C
• 
  D

The transport of a rectangular matrix is a

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

• 0 A
• 1 B
• 2 C
• 3 D

• Symmetric A
• Skew-symmetric B
• Hermitian C
• Skew hermitian 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