Evaluate

Theorem: This evaluation can be done in two different ways either by taking out the common things and then calculating the determinants or simply take determinant.


I will prefer first method because with that chances of silly mistakes reduces.


Take out x+1 from second row.


(x+1) ×


⇒(x+1) × (x2-x+1-(x-1))


⇒ (x+1) × (x2-2x+2)


⇒ x3-2x2+2x+x2-2x+2


⇒ x3-x2+2 .


1