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13. (a) Show that the system
 
 

 has a solution if the a, b, c are distinct and 
 
(b) Calculate the solution.
 

14. Evaluate:
 
(a) 
 
(b) 
 
(c) 
 
 15. Let D be the general n by n Vandermonde determinant with the entry cij in the ith row and jth column given by cij = aji-1. Show that D is the product
 

(a2 - a1)(a3 - a1)(a3 - a2)...(an - an-1)
 
of all the different ar - as with 
 
 
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Tuesday, June 23, 1998