Prepare for a short quiz.
Let R(s, t) be the function from R^{2} to R^{3} defined by
| R(s, t) = (s + 2 t, -2 s - t, -2 s + 2 t) . |
Find equation(s) that characterize the set S of all points (x, y, z) in R^{3} that arise as R(s, t) for at least one pair (s, t).
What kind of subset of R^{3} is S ?