ISRO 2013- Matrices /Mech

Question

Tha matrix $ \begin{bmatrix} 0 & -4 &1 \\ 4& 0 &-5 \\ -1&5 &0 \end{bmatrix} $is

 

(a) Orthogonal Matrix
(b) Skew Symmetric

(c) Symmetric

(d) Idempotent

Answer 1

1- Its is Not Idempotent as it does not satisfy Idempotent Property(In algebra, an idempotent matrix is a matrix which, when multiplied by itself, yields itself.That is, the matrix M is idempotent if and only if MM = M. For this product MM to be defined, M must necessarily be a square matrix. ). 

2- It is not Orthogonal as it does not satisfy Orthogonal Property(  In linear algebra, an orthogonal matrix or real orthogonal matrix is a square matrix with real entries whose columns and rows are orthogonal unit vectors ,) .

3- Check for Symmetric

It is not Symmetric

4- Check For Skew Symmetric

a_ij = −a_ji.

It is Skew Symmetric

Hence B is Correct Answer.

Answer 2

Just check out Skew Symmetric matrix Condition: A= -(A^T)

where A^T= transpose of matrix.

U will get answer Skew Symmetric matrix

Ans:B)