10.

Solution: Assume there be a system of n simultaneous linear equations and with ‘n’ unknown given by

Let be the determinant obtained from D after replacing the column by

Then,

provided that

So by comparing with the theorem, let’s find

Solving for the determinant, expanding along 1^st row

Again,

Solving for the determinant, expanding along 1^st row

Solving for the determinant, expanding along 1^st row

⇒ 

⇒ 

⇒ 

Therefore, by Cramer’s Rule, we will get

And