(c) (4%)If the basis is γ, find the dimension of ker(T) and the basis of ker(T).

26. (4%) Use generating functions to prove Pascal's identity:C(n,r)=C(n-1,r)+C(n-1,r-1) when n and r are positive integers with r ＜ n.(Hint: Use the identity (1 +x)n=.]

27. (5%) Let (Xi, yi), i = 1,2,3,4,5, be a set of five distinct points with integer coordinates in the xy plane. Show that there is at least one of the midpoints of the segment joining of these points which has integer coordinates.

(a) (6%)Find [T]βand [T]γ.

(b) (6%)Find the matrix S such that.

110年 - 110 國立政治大學_碩士班暨碩士在職專班招生考試_資訊科學系:計算機數學#108089