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

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

• A A
• A' B
• -A C
• A D

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

• A^- A
• A^t B
• -A C
• A 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

Rank of matrix [1 3 5 0] is

• 1 A
• 3 B
• 2 C
• 4 D

• I A
• 14 I B
• 0 C
• None of these D

• -a -b -c A
• 1 B
• 0 C
• -1 D

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

Which of the following is an identity matrix?

• 
  A
• 
  B
• 
  C
• none of these D

Trival solution of homogeneous linear equation is

• (0, 0, 0) A
• (1, 2, 3) B
• (1, 3, 5) C
• a.b and c 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

• 
  A
• 
  B
• 
  C
• 
  D

• 1, 2, 3 A
• 1, 5, 9 B
• 2, 5, 8 C
• 3, 6, 9 D

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

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

• 
  A
• 
  B
• 
  C
• 
  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

• 0 A
• 1 B
• -A C
• -1 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

• A(α) - A(β) A
• A(α) + A(β) B
• A(α-β) C
• A(α+β) D

• 9/4 A
• 4/9 B
• 1 C
• None of these D

For non-trival solution |A| is

• A = 0 A
• A^t= 0 B
• |A| = 0 C
• None of these D

Cofactor of an element aij denoted by Aij is

• (-2)i+j A
• Mij B
• (-1)i+j Mij C
• None of above D

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

• 
  A
• 
  B
• 
  C
• 
  D

• 16 A
• 256 B
• 64 C
• 1024 D

• 
  A
• 
  B
• 
  C
• 
  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

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