Mathematics ECAT Pre Engineering Chapter 5 Matrices and Determinants Online Test

For non-trival solution |A| is

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

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

Minor of an element a_ijis denoted by

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

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

The transpose of a column matrix is a ______

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

(ABC)' =

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

Matrix multiplication is

• Commutative A
• Not commutative B
• Not associative C
• Not distributive 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

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

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

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

If A is singular then |A| = ______

• 1 A
• 0 B
• 2 C
• None of these D

• 1 A
• 0 B
• -1 C
• 2 D

• At A
• -A B
• A C
• A-1 D

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

A matrix in which the number of rows is not equal to the number of columns is called a

• Diagonal matrix A
• Rectangular matrix B
• Square matrix C
• Scalar matrix D

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

If A = |aij| 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

• 
  A
• 
  B
• 
  C
• 
  D

Every identity matrix is

• Row-vector A
• Scalar B
• Column-vector C
• All D

An equation of the form ax + by = k is homogeneous linear equation when:

• 
  A
• 
  B
• 
  C
• 
  D

The matrix A is Hermitian when (A)' =

• A A
• -A B
• A C
• A' D

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

• 
  A
• 
  B
• 
  C
• 
  D

• a = 4, b = 1 A
• a = 1, b = -4 B
• a = 0, b = 4 C
• a = 2, b = 4 D

Which of the following is skew symmetric matrix

• 
  A
• 
  B
• 
  C
• 
  D

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

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