The column of I_{2} = \(\begin{bmatrix}1 & 0\\ 0 & 1\end{bmatrix}\) are (e_{1}) = \(\begin{bmatrix}1\\ 0\end{bmatrix}\), and e_{2} = \(\begin{bmatrix}0\\ 1\end{bmatrix}\). Suppose T is a linear transformation from R^{2} into R^{3} such that

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

find a formula for the image of an arbitrary x in R^{2}. That is, find T(x) for x in R^{2}.

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