Consider the triangle Δ in R3 with corners (1, 0, 0), (0, 1, 0), (0, 0, 1).
(a) Find the image of Δ under the projection that sends (x, y, z) ∈ R3 7→ (x, y) ∈ R2. Is this a linear transformation?
(b) What is the area of the image of Δ after the projection?
(c) Is there a linear transformation that will send Δ to the xy-plane so that the image has the same area as Δ, and one of the corners of the image is (0, 0)?
