The column of I₂ = \(\begin{bmatrix}1 & 0\\ 0 & 1\end{bmatrix}\) are (e₁) = \(\begin{bmatrix}1\\ 0\end{bmatrix}\), and e₂ = \(\begin{bmatrix}0\\ 1\end{bmatrix}\). Suppose T is a linear transformation from R² into R³ such that

T(e₁) = \(\begin{bmatrix}5\\ 1\\ -2\end{bmatrix}\) and T(e₂) = \(\begin{bmatrix}0\\ -1\\ 8\end{bmatrix}\)

find a formula for the image of an arbitrary x in R². That is, find T(x) for x in R².