Find the area of region R

Question

Let D be the disk of radius 2 in the uv-plane. Let R is subset of R² be the image of D under the transformation:

x=2u +3v, y=-u+2v.

Find the area of R.

Answer 1

You just calculate the determinant of the transformation, and multiply the absolute value of this times the area of the original disk.

2 3

-1 2

has determinant 4 + 3 = 7

Thus, the area is 7 * 4 pi = 28 pi