You may use any results which were proved in class or in the textbook provided that you state them clearly. You may not use results which were proved as part of your homework unless you prove them again here. T : p2(r) p3(r) f 7 z f (x) dx. Question 3 (15 points: state and prove the dimension theorem, let. Show that w0 is a subspace of pn(r) and that w1 is not: find the dimension of w0. Let v be the vector space of smooth functions from r to r. let. Question 4 (5 points each part) g1 : v r f 7 f (1) g2 : v r f 7 f (2) h : v r f 7 z 1. A linear map t : v v from a vector space v to itself is called left-invertible if and only if there exists a map s : v v such that st = iv .
