Detailed solution to Problem Set 25 Exercise 5

Question:

Evaluate dx ∧ dy along d(x, y) = ⟨−2, 3⟩, ⟨4, 6⟩.

Solution:

(dx ∧ dy)|_{d(x, y)=⟨−2, 3⟩, ⟨4, 6⟩} = dx|_{⟨dx, dy⟩=⟨−2, 3⟩} ⋅ dy|_{⟨dx, dy⟩=⟨4, 6⟩} − dy|_{⟨dx, dy⟩=⟨−2, 3⟩} ⋅ dx|_{⟨dx, dy⟩=⟨4, 6⟩} = (−2)(6) − (3)(4) = −24.

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