In each case determine whether U is a subspace of R3. Support your answer.
U={[r s t] | r,s, and t in R, -r+3s+2t=0}.
Or just show that the set is closed under addition and scalar multiplication.
If [r, s, t] is in that set then -r+3s+2t=0. If [u, v, w] is in that set, then -r+ 3v+ 2w= 0.
What about [r+ u, s+ v, t+ w]? Does it satisfy that equation?
What about [ar, as, at] for some number a? Does it satisfy that equation?