# Find a transformation from u,v space to x,y,z space that takes the triangle U = [(0,0),(1,0),(0,1)] to the triangle T=[(1,0),-2),(-1,2,0),(1,1,2)]

Find a transformation from u,v space to x,y,z space that takes the triangle $U=\left[\begin{array}{cc}0& 0\\ 1& 0\\ 0& 1\end{array}\right]$ to the triangle
$T=\left[\left(1,0\right),-2\right),\left(-1,2,0\right),\left(1,1,2\right)\right]$