The columns of I2 = beginbmatrix 1 & 0 0 & 1 endbmatrix are e1 = beginbmatrix 1 0 endbmatrix and e2 = beginbmatrix 0 1 endbmatrix. Suppose T is a linear transformation from mathbbR2 into mathbbR3 such that T(e1) = beginbmatrix 5 1 -2 endbmatrix, T(e2) = beginbmatrix 0 -1 8 endbmatrix Find a formula

The columns 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 $\mathbb{R}^2$ into $\mathbb{R}^3$ such that $T(e_1) = \begin{bmatrix} 5 \ 1 \ -2 \end{bmatrix}$, $T(e_2) = \begin{bmatrix} 0 \ -1 \ 8 \end{bmatrix}$

Find a formula for the image of an arbitrary $x$ in $\mathbb{R}^2$. That is, find $T(x)$ for $x$ in $\mathbb{R}^2$. [2.5+2.5]