Question

1: We define the Vandermonde Determinant, denoted V(ai,a2,... ,an), as ai a...a-1 1 2 i a2 az...a-1 al,a2 ,an ) 2. 1 an a an ...an-1 We will guide you through a proof by Mathematical Induction to show that V(a,aan) aj -ai f: Show that if we perform k Type 3 ccolumn operations by adding a multiple B, of col- umn i, where1,2,. ,k, to the last column, then the Vandermonde determinant of size (k 1) x (k 1) can be written as:

Answer 1

n-2 or n-2. v- is true or », Assume t is 뇨-1 I a1 0 Le-i I a -A.a

1st r… and factoring ai-ai rom we have İ: 2, 3,.., kt, or 2. 2. ktl ar-a 0 k서 y Inductton h >ohess, e have Thus,沙is also true bor n a -a