ECAT Pre Engineering MCQ Test With Answer for Chapter 5 Mathematics

For a square matrix A, if A = At, then A is called

• Matrix A
• Transpose B
• Symmetric C
• Non-symmetric D

If A is singular then |A| = ______

• 1 A
• 0 B
• 2 C
• None of these D

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

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

• 2 A
• 4 B
• 6 C
• 8 D

Two matrices A and B are conformable for the product AB if

• Both A and B are square A
• Both A and B are symmetric B
• Number of rows of A = number of columns of B C
• Number of columns of A = number of rows of B D

Matrices are represented by

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

• 
  A
• 
  B
• 
  C
• 
  D

The number of non zero rows in echelon form of a matrix is called

• Order of matrix A
• Rank of matrix B
• Row operation C
• None of these D

The matrix A is Hermitian when (A)' =

• A A
• -A B
• A C
• A' D

• A A
• -A B
• A^t C
• A^- D

A = [3] is a/an

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

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

• 
  A
• 
  B
• 
  C
• 
  D

• 1 A
• 0 B
• -1 C
• 2 D

• k3 A
• 0 B
• 3k C
• k6 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 square matrix A = [aij] is lower triangular matrix when

• aij = 0 for all i<j A
• bij = 0 B
• cij = 0 C
• dij = 0 D

• 
  A
• 
  B
• 
  C
• 
  D

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

• A2 A
• A3 B
• A C
• None of above D

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

A square matrix A for which A^t= A is called a

• Column matrix A
• Symmetric matrix B
• Skew-symmetric matrix C
• Row matrix D

• A²- 5A + 7I = 1 A
• 2A²- 3A + 7I = 0 B
• A²- 5A + I = 0 C
• A²- 5A + 7I = 0 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

• 
  A
• 
  B
• 
  C
• 
  D

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

For any positive integer n

• ABn = Bn A ⇔ AB = BA A
• ABn = Bn A⇔ A,B are square matrices and AB = BA B
• ABn = BnA⇔ A + B C
• ABn = BnA ⇔ A and B are square matries 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 = 2, b = 3 A
• a = 3, b = 2 B
• a = 2, b = 1, 2 C
• a = 3, b = 3 D

• 
  A
• 
  B
• 
  C
• 
  D