ECAT Mathematics Chapter 5 Matrices and Detarminants Online Test

In order of A is m x n and order of B is n x p then order of AB is

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

• 
  A
• 
  B
• 
  C
• 
  D

• I3 A
• rI3 B
• r C
• none D

If A is any matrix then its additive inverse is

• A A
• A^-1 B
• A^t C
• -A D

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

If order of A is m x n, then order of A^tis

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

Cofactor of an element a_ijis defined by

• (-1)^i+j|A| A
• (-1)^i+jM_ij B
• (-1)^i+jM^-1 C
• None of these D

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

If A is skew Hermitian Matrix then which of the following is not skew Hermitian matrix

• A2 A
• A5 B
• A3 C
• A7 D

• 
  A
• 
  B
• 
  C
• all are correct D

• -a -b -c A
• 1 B
• 0 C
• -1 D

• 
  A
• 
  B
• 
  C
• 
  D

A matrix with a single row is called a

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

A diagonal matrix is always

• Identity A
• Triangular B
• Scalar C
• Non-singular D

• 1 A
• 0 B
• -1 C
• 2 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

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

• x =0, y =4 A
• x = -1, y = 2 B
• x = 2, y = 3 C
• x = 3, y = 4 D

• 
  A
• 
  B
• 
  C
• 
  D

The square matrix A is skew-symmetric when At=

• -B A
• -C B
• -A C
• -D 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

• Orthogonal A
• Involutary B
• Idempotent C
• Nilpotent 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

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

• Symmetric A
• Skew-symmetric B
• Hermitian C
• Skew hermitian D

Matrices are represented by

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

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

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