please show all work! Thank you! Question 2 (6 points). Let VW be vector spaces over the field R, and let L V W be a linear map Show that the following two statements are equivalent: (a) L is 1-1. (b) for z in V, if L (z) 0, then 0. Hint: Use the fact that Lis linear and L (0) 0.] Solution a) Given that L is linear i.e. L(x+y) = L(x)+L(y) Let L(a) = L(b) Then L(a-b) = L(a)-L(b) =0 L(a-b) =0 But L(a-a) = L(a)-L(a) =0 Hence L(a-b) = L(a-a) This implies a = b and also L(X) =0 means only for x =0.