Suppose that $S_1$ and $S_2$ are nonzero subspaces, with $S_1$ contained inside $S_2$, and suppose that $dim(S_2) = 3$.
(a) What are the possible dimensions of $S_1$? ? 1 2 3 1 or 2 1,2, or 3
(b) If $S_1\neq S_2$ then what are the possible dimensions of $S_1$? ? 1 2 3 1 or 2 1,2, or 3