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

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

For trival solution |A| is

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

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

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

If A is any matrix then its additive inverse is

• A A
• A^-1 B
• A^t C
• -A D

The transport of a rectangular matrix is a

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

• 
  A
• 
  B
• 
  C
• 
  D

The matrix A = [aij]mxn with m ≠n is always

• Symmetric A
• Hermition B
• Skew-symmetric C
• None 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 diagonal matrix in which the diagonal elements are equal is called a

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

• At A
• -A B
• A C
• A-1 D

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

The transpose of a zero matrix is a ______

• Column matrix A
• Zero matrix B
• Row matrix C
• Scalar 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

• A^- A
• A^t B
• -A C
• A D

• Orthogonal A
• Involutary B
• Idempotent C
• Nilpotent D

If A is singular then |A| = ______

• 1 A
• 0 B
• 2 C
• None of these D

We solve the system of non-homogeneous linear equations by

• a and b A
• b and c B
• c and a C
• a,b and c D

• 
  A
• 
  B
• 
  C
• 
  D

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

If A = [aij]mxpand B =[aij]pxnthen order of BA is

• m x n A
• p x n B
• n x m C
• None of these D

• 4A - 3I A
• 3A - 4I B
• A - I C
• None of these D

• 
  A
• 
  B
• 
  C
• 
  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

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

For a square matrix A, if A = A^t, then A is called

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

• k3 A
• 0 B
• 3k C
• k6 D

The matrix A is Hermitian when (A)' =

• A A
• -A B
• A C
• A' D

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

• A2 A
• A3 B
• A C
• None of above D