2. (36 points) In each case determine if the given subset W of a vector space V is a subspace. Justify your answer. (a) V=R3, W={(x1,x2,x3)| 2:L'12:c2+a:3=0}; (b) V=R3, W={(a+b,ab,ac) | a,b,cE]R}; (C) V=R4, W={(.T1,.'L'2,$3,:174) I 2$12C2 +123 +$4=5}; (d) V = M2X2(R), the vector space of all 2 x 2 matrices, W = {A E V |A2 = A}, the subset of all idempotent matrices; (e) V = MnanR), the vector space of all n x n matrices and W = {A E V |A is singular}; (f) V = MnxnR), the vector space of all n X n matrices and W = {A E V | tr(A) = 0}, that is, W consists of all n x n matrices Whose trace is equal 0