Find a General Formula of a Linear Transformation From $\R^2$ to $\R^3$
Problem 353
Suppose that $T: \R^2 \to \R^3$ is a linear transformation satisfying
\[T\left(\, \begin{bmatrix}
1 \\
2
\end{bmatrix}\,\right)=\begin{bmatrix}
3 \\
4 \\
5
\end{bmatrix} \text{ and } T\left(\, \begin{bmatrix}
0 \\
1
\end{bmatrix} \,\right)=\begin{bmatrix}
0 \\
0 \\
1
\end{bmatrix}.\]
Find a general formula for
\[T\left(\, \begin{bmatrix}
x_1 \\
x_2
\end{bmatrix} \,\right).\]
(The Ohio State University, Linear Algebra Math 2568 Exam Problem)
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