3. (20 points) (a) Find the one-forms mapped by the metric tensor from the vectors
$\vec{A} \to (1, 0, -1, 0)$,
$\vec{B} \to (0, 1, 1, 0)$,
$\vec{C} \to (-1, 0, -1, 0)$,
$\vec{D} \to (0, 0, 1, 1)$.
Homework No. 7
(b) Find the vectors mapped by the inverse of the metric tensor from the one-forms
$\vec{p} \to (3, 0, -1, -1)$,
$\vec{q} \to (1, -1, 1, 1)$,
$\vec{r} \to (0, -5, -1, 0)$,
$\vec{s} \to (-2, 1, 0, 0)$.