ECAT Pre General Science Chapter 5 MCQ Test With Answer for Mathematics chapter 5 (Matrics and Determinants)

• An upper triangular matrix A
• A lower triangular matrix B
• A diagonal matrix C
• A null matrix D

• (2x+a+b+c) A
• (a+b+c) B
• (a+b+c+x) C
• 0 D

• 
  A
• 
  B
• 
  C
• 
  D

• At A
• -A B
• A C
• A-1 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

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

• A2 A
• A3 B
• A C
• None of above D

A diagonal matrix in which the diagonal elements are equal is called a

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

• 
  A
• 
  B
• 
  C
• 
  D

• I3 A
• rI3 B
• r C
• none D

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

• BA A
• A2 B
• AB C
• B2 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

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

• 1 A
• 0 B
• -1 C
• 2 D

If A and B are skew-symmetric then (AB)t is

• At Bt A
• AB B
• -AB C
• BA D

A matrix with a single column is called

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

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

• A² A
• A³ B
• A C
• None of above D

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

• 
  A
• 
  B
• 
  C
• 
  D

• 
  A
• 
  B
• 
  C
• 
  D

• 3K A
• K2 B
• K3 C
• K D

• 
  A
• 
  B
• 
  C
• all are correct D

If the matrices A and B have the order 1 x 10 and 10 x 1 then order of AB is

• 1 x 1 A
• 1 x 10 B
• 10 x 10 C
• 10 x 1 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

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

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

• 1, 2, 3 A
• 1, 5, 9 B
• 2, 5, 8 C
• 3, 6, 9 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 transport of a rectangular matrix is a

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