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

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

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

• 
  A
• 
  B
• 
  C
• 
  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

• 0 A
• Independent of a B
• Independent of b C
• Independent of c D

(ABC)' =

• CBA' A
• CBA B
• C' B' A' C
• None of these 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

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

The square matrix A is skew-symmetric when At=

• -B A
• -C B
• -A C
• -D D

If there are m rows and n columns in a matrix then its order is

• m x n A
• m x m B
• n x n C
• n x m D

For non-trival solution |A| is

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

The transport of a null matrix is

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

• I3 A
• rI3 B
• r 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
• 
  B
• 
  C
• 
  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

For non-trival solution |A| is

• non zero A
• A = 0 B
• |A| = 0 C
• At = 0 D

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

• 0 A
• 1 B
• 2 C
• 3 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

System of linear equations is inconsistent if

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

If A and B are two matrices such that AB = B and BA =A, then A²+ B²=

• 2 AB A
• 2 BA B
• A + B C
• AB 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

• a = 2, b = 3 A
• a = 3, b = 2 B
• a = 2, b = 1, 2 C
• a = 3, b = 3 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

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

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
• 
  B
• 16 C
• None of these D