Chapter 1.8, Problem 19E

Let ${\text{e}}_1=\left[\begin{array}{c}1\\ 0\end{array}\right]$, ${\text{e}}_2=\left[\begin{array}{c}0\\ 1\end{array}\right]$, ${\text{y}}_1=\left[\begin{array}{c}2\\ 5\end{array}\right]$, and ${\text{y}}_2=\left[\begin{array}{c}-1\\ 6\end{array}\right]$, and let T : ℝ² ⟶ ℝ² be a linear transformation that maps e₁ into y₁ and maps e₂ into y₂. Find the images of $\left[\begin{array}{c}5\\ -3\end{array}\right]$ and $\left[\begin{array}{c}{x}_1\\ x_2\end{array}\right]$.