ECAT Pre Engineering MCQ Test With Answer for Chapter 5 Mathematics

The matrix A = [aij]mxn with m≠n is

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

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

• 0 A
• 1 B
• -2 C
• 10 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

• Orthogonal A
• Involutary B
• Idempotent C
• Nilpotent D

• 2s² A
• 2s³ B
• s³ C
• 3s³ 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

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

• a = 4, b = 1 A
• a = 1, b = -4 B
• a = 0, b = 4 C
• a = 2, b = 4 D

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

For trival solution |A| is

• A A
• |A| = 0 B
• A = 0 C
• |A|≠ 0 D

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

• 
  A
• 
  B
• 
  C
• 
  D

We also 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

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 = [3] is a/an

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

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

If A is any matrix then its additive inverse is

• A A
• A^-1 B
• A^t C
• -A D

• At A
• -A B
• A C
• A-1 D

• 9/4 A
• 4/9 B
• 1 C
• None of these D

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

• 
  A
• 
  B
• 
  C
• 
  D

• 
  A
• 
  B
• 
  C
• 
  D

The transpose of a column matrix is a ______

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

Which of the following is an identity matrix?

• 
  A
• 
  B
• 
  C
• none of these D

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

• -3 A
• -7 B
• 1 C
• 0 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

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

• 1 A
• 0 B
• 3 C
• -1 D