Determine if the following sets are subspaces of R3 or not and justify.

a) V={ [x1,x2,x3] | x3 = 1+x1 }

b) W={ [a-b, 2b, 3c-a] | a,b,c R(real) }

note: x1,x2,x3 and a-b,2b,3c-a are column vectors

I think for a) it is not because the zero vector is not present and for b) it is since W = span {[1,0,-1],[-1,2,0],[0,0,3]}

What do you think?