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Homework Statement
Let ##T:ℝ^3→ℝ^2## be the linear transformation defined by ##\begin{bmatrix}
x_1 \\
x_2 \\
x_3
\end{bmatrix}\mapsto \begin{bmatrix}
x_1 + x_2 + x_3\\ 0
\end{bmatrix}##.
i. Find the standard matrix for ##T##.
Homework Equations
The Attempt at a Solution
For this problem I was able to guess that the standard matrix is ##\begin{bmatrix}
1&1&1 \\
0&0&0\end{bmatrix}## (at least I think it is), but what I'd really like to understand is how to find it without simply guessing.
I've tried something like:
##A \begin{bmatrix}x_1\\x_2\\x_3 \end{bmatrix} = \begin{bmatrix} x_1+x_2+x_3\\0\end{bmatrix}##
##A=\begin{bmatrix} x_1+x_2+x_3\\0\end{bmatrix}\begin{bmatrix}x_1\\x_2\\x_3 \end{bmatrix}^{-1}##
But that doesn't work since the right side can't undergo matrix multiplication. I'm not sure what else to do.