ECAT Pre General Science MCQ Test With Answer for Mathematics Chapter 5

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

The transport of a square matrix is a

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

For trival solution |A| is

• A A
• |A| = 0 B
• A = 0 C
• |A|≠ 0 D

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

A matrix with a single column is called

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

If A is singular then |A| = ______

• 1 A
• 0 B
• 2 C
• None of these D

The square matrix A is skew-symmetric when At=

• -B A
• -C B
• -A C
• -D 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
• 
  B
• 
  C
• 
  D

• 0 A
• abc B
• 1/abc C
• None of these D

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

• 
  A
• 
  B
• 
  C
• 
  D

• 
  A
• 
  B
• 
  C
• 
  D

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

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

• 0 A
• 1 B
• -A C
• -1 D

• 
  A
• 
  B
• 
  C
• 
  D

• Singular A
• Non-singular B
• Adjoint C
• None of above D

• -a -b -c A
• 1 B
• 0 C
• -1 D

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

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

• A A
• A' B
• -A C
• A D

• 1 A
• 0 B
• 3 C
• -1 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

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

• 2s² A
• 2s³ B
• s³ C
• 3s³ 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

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^- A
• A^t B
• -A C
• A D

The transport of a null matrix is

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