We need to find the following with linear Algebra

Let {61,62} be a orthonormal basis of R2. (That is, (61,62) = elTeg = 0 and (ehei) = T61: 1 for i = 1, 2.) Dene a map F : R2 > R2 as follows: 6i 2 F(x) = Z A(e,x)e i=1 where M 6 R and (61-, ac) = ellx is the dot product between vectors ei and x. a) Show that F is a linear transformation. b) Obtain conditions on M such that F(x) = 0 for all a: E R2. 0) Obtain conditions on Ai such that F is 1-1. d) Obtain conditions on M such that F is onto. e) [Extra credit] How do your answers to parts (a)-(d) change if {61,62} is simply a basis (not necessarily orthonormal)