(a) Find the one-forms mapped by the metric tensor from the vectors O (1, 0, -...

Question:

(a) Find the one-forms mapped by the metric tensor from the vectors
→ O (1, 0, - 1, 0)
→ O (1, 0, - 1, 0)
→ O (-1, 0, - 1, 0)
→ O(0, 0, 0, 1, 1).
(b) Find the vectors mapped by the inverse of the metric tensor from the one-form
→ O (3, 0, −1, −1),
→ O (1, −1, 1, 1),
→ O (1, −5, -1, 0),
→ O (-2, 1, 0, 0)?