(after 3.1) Say we have linear transformations T : R 3 → R 2 and S : R 2 → R 4 . Let S ◦ T : R 3 → R 4 be the composition (that is, R 3 T −−→ R 2 S −−→ R 4 ). Can S ◦ T be one-to-one? (Hint: Start by thinking about all x such that T(x) = 0.)