Chapter 6.1, Problem 28P

For Problems 27-30, assume that $T$ defines a linear transformation and use the given information to find the matrix of $T$.

$T:{ℝ}^4\to {ℝ}^2$, such that $T\left(1,0,0,0\right)=\left(3,-2\right)$, $T\left(1,1,0,0\right)=\left(5,1\right)$, $T\left(1,1,1,0\right)=\left(-1,0\right)$ and $T\left(1,1,1,1\right)=\left(2,2\right)$.