show or refute the sets: a) U = \left \{x = (x_1,x_2,x_3)^T \in R^3 : x_2+x_2+x_3 = 0 \right \} forms a subspace ofR^3, determine the dimension ofU b) is there a set M with u distinct vectors i.e a,b,c,d\in R^3​​​​​​​ such that every 3 elements of M are linearly independent? give such an example