ECAT Pre Engineering MCQ Test With Answer for Chapter 5 Mathematics

• 
  A
• 
  B
• 
  C
• all D

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

• 
  A
• 
  B
• 
  C
• 
  D

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

• At Bt A
• AB B
• -AB C
• BA 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

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

• A² A
• A³ B
• A C
• None of above D

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

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

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

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 transport of a square matrix is a

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

• 2 A
• 4 B
• 6 C
• 8 D

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

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

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

• A A
• A' B
• -A C
• A D

• 3 x 1 A
• 1 x 3 B
• 3 x 3 C
• 1 x 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

• 
  A
• 
  B
• 
  C
• 
  D

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

The transpose of a row matrix is a ______

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

A square matrix all of whose elements except the main diagonal are zeros is called a

• Null matrix A
• Singular matrix B
• Symmetric matrix C
• Diagonal matrix D

• 
  A
• 
  B
• 
  C
• 
  D

• 
  A
• 
  B
• 
  C
• 
  D

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

System of linear equation is inconsistent if

• System has no solution A
• System has one solution B
• System has two solution C
• None of above D

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

Let A is a 3 x 3 matrix and B is its adjoint matrix. If |B| = 64, then |A| =

• 
  A
• 
  B
• 
  C
• 
  D

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

• A2 A
• A3 B
• A C
• None of above D