MA 35100 Lecture Notes - Lecture 12: Solution Set, Linear Independence, Linear Combination
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: let w be the set of all functions f in c (r) such that f " (2) = 0 . Show that w is a subspace of c. r. F in c - r whose derivative evaluated at = 2 is 0 . Let f) g e w [ f " (2) = 0 , g" (2) = 0] " (x) ; so at = 2 , (ftg) (2) = 0. Let f e w [ f " (2) = 0] . Let s be a scalar . ( sf) " (x) = sf"( ) sf " (2) = 0. 0 which is 0 at = 2s. Spans are subspaces so column space , null space are subspaces ; you can also try that using the above methods . How to figure out if a given set s is linearly (in) dependent : alt . An } is 1in . inaep . iff ,
