Question 2. (10 pTs) Let V be a vector space over K. a) (5 pr1S) Let {w;,...,w;} be linearly independent in V and let v V. Prove by definition of linear independence that v Span{w,,..., wy } if and only if {v,w,,...,w;} is still linearly independent. Note. To prove \"A if B\" you need to show B=A, that is when B is true A must also be true; To prove \"A only if B\" you need to show A=B. b) (5 PTS) Let S be finite. Let T C S be a set of vectors that is linearly independent. Prove that there is a finite collection of vectors B satisfying T'C B C S such that B is linearly independent and Span(B) = Span(S)