ECAT Pre Engineering Mathematic MCQ Test With Answer for Chapter 5 (Matrices and Determinants)

Every identity matrix is

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

• 
  A
• 
  B
• 
  C
• 
  D

For trival solution |A| is

• A A
• |A| is non zero B
• A = 0 C
• None of these 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

• 
  A
• 
  B
• 16 C
• None of these D

• 1 A
• 0 B
• -1 C
• 2 D

• 0 A
• 1 B
• -A C
• -1 D

• 
  A
• 
  B
• 
  C
• 
  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

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

• 
  A
• 
  B
• 
  C
• 
  D

If A = [a_ij] is (m x n) matrix, then transpose of A is of the order

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

• Identity matrix A
• Diagonal matrix B
• Null matrix C
• Hermitian matrix 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

• K/6 A
• 2K B
• 3K C
• 6K D

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

• A² A
• A³ B
• A C
• None of above D

• 2s² A
• 2s³ B
• s³ C
• 3s³ 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

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

A matrix with a single row is called a

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

• I A
• |A| B
• |A| I C
• None of these D

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

The square matrix A is skew-symmetric when At =

• -B A
• -C B
• -A C
• -D D

If A is a non singular matrix then A^-1= ______

• 
  A
• 
  B
• 
  C
• 
  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

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

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

• a = 2, b = 3 A
• a = 3, b = 2 B
• a = 2, b = 1, 2 C
• a = 3, b = 3 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

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

• 
  A
• 
  B
• 
  C
• 
  D

• 3 x 1 A
• 1 x 3 B
• 3 x 3 C
• 1 x 1 D