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

• 
  A
• 
  B
• 
  C
• 
  D

• 1 A
• 0 B
• -1 C
• 2 D

The order of the matrix [1 2 3] is

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

A matrix in which the number of rows is equal to the number of columns is called a

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

• 3K A
• K2 B
• K3 C
• K D

The transport of a rectangular matrix is a

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

Matrices A = [aij] 2 x 3 and B =[bij] 3 x 2 are suitable for

• BA A
• A² B
• AB C
• B² D

The transpose of a zero matrix is a ______

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

• 
  A
• 
  B
• 
  C
• 
  D

• 9/4 A
• 4/9 B
• 1 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

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

If A = |aij| 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

The square matrix A is skew-symmetric when At =

• -B A
• -C B
• -A C
• -D D

The transport of a null matrix is

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

Minor of an element a_ijis denoted by

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

• 5 A
• 
  B
• -5 C
• none D

• a = -1/2, b = -1 A
• a = 1, b = 2 B
• a = 2, b = 3 C
• None of above 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

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

The square matrix A is skew Hermitian when (A)'=

• A A
• A' B
• -A C
• A D

• 
  A
• 
  B
• 
  C
• 
  D

• 0 A
• 1 B
• 2 C
• 4 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

The order of the matrix A is 3 x 5 and that of B is 2 x 3.The order of the matrix BA is

• 2 x 3 A
• 3 x 2 B
• 2 x 5 C
• 5 x 2 D

The matrix A is Hermitian when (A)' =

• A A
• -A B
• A C
• A' D

• 1 A
• -1 B
• 0 C
• I D