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

The matrix A is Hermitian when (A)' =

• A A
• -A B
• A C
• A' 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

For non-trival solution |A| is

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

If A is singular then |A| = ______

• 1 A
• 0 B
• 2 C
• None of these D

Which of the following is an identity matrix?

• 
  A
• 
  B
• 
  C
• none of these D

Minor of an element a_ijis denoted by

• M_ij A
• A_ij B
• |A| C
• None of these D

• I3 A
• rI3 B
• r C
• none D

We also 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

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 non-homogeneous linear system AX = B has no solution if

• |A| = 0 A
• |A|≠ 0 B
• Rank (a) = no of variables C
• Rank > no of variables D

A matrix with a single row is called a

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

• 0 A
• 1 B
• -2 C
• 10 D

The transpose of a row matrix is a ______

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

• 
  A
• 
  B
• 
  C
• 
  D

A diagonal matrix is always

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

• 
  A
• 
  B
• 
  C
• 
  D

• 
  A
• 
  B
• 
  C
• 
  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

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

• a²b²c² A
• 4a²b²c² B
• 4abc C
• None D

(ABC)' =

• CBA' A
• CBA B
• C'B'A C
• C'B'A' 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

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

For trival solution |A| is

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

The transpose of a zero matrix is a ______

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

• 
  A
• 
  B
• 
  C
• 
  D

Matrices are represented by

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