Chapter 5.7, Problem 389E

The triangular region R with the vertices (0, 0). (2, 0), and (1. 3) is shown in the following figure.

Find a transformation $T:S\to R$ . $T\left(u,v\right)=\left(x,y\right)=\left(au+bv,cu,dv\right)$where a. b. c and d are real numbers with $ab-\ne 0$

such that $T^{-1}\left(0,0\right)=\left(0,0\right),T^{-1}\left(2,0\right)=\left(1,0\right)$ , and $T^{-1}\left(1,3\right)=\left(0,1\right)$ .

b. Use the transformation T to find the area A(R) of the region R.