Question

Show that elements on the main diagonal of a skew-symmetric matrix are all zero.

Answer 1

solution of the above problem

Answer 2

Answer:

Elements on the main diagonal of a skew - symmetric matrix are all zero proved .

Step-by-step explanation:

Explanation:

Skew -symmetric matrix -A square matrix that has its transpose equal to its negative is said to be skew-symmetric .

Let us suppose that a = [$a_{ij}$] be a skew -symmetric matrix then ,

[$a_{ij}$ ] = [$-a_{ij}$] for all value of i and j .

The elements are in diagonal , so substitute i = j .

In square matrix diagonals elements are $a_{ii} , a_{22} and \ a_{33}$ .

⇒ $2a_{ii}$ = 0  ⇒$a_{ii}$ = 0

Similarly , $a_{22} = a_{33}$ = 0

Therefore ,  $a_{11} = a_{22}= a_{33}$ = 0 .

Final answer:

Hence , here we showed that element on the main diagonal of a skew - symmetric matrix  are all zero.

#SPJ2