Trying to review for a quiz and I'm woefully underprepared.
Question is:
For each of the following linear transformations $L$ mapping $\mathbb{R}^3$ into $\mathbb{R}^2$, find a matrix $A$ such that $L(x) = Ax$ for every $x$ in $\mathbb{R}^3$.
a) $L((x_1, x_2, x_3)^T) = (x_1 + x_2, 0)^T$
I don't quite know how to approach this problem. It's probably very simple, but the change from $\mathbb{R}^3 \to \mathbb{R}^2$ or from $\mathbb{R}^2 \to \mathbb{R}^3$ confuses me, I'm not sure how to treat it.
I'm looking for a slow demonstration of steps rather than an actual answer. Calculations are nice, but I'd rather learn the steps and reasoning behind them so I can complete these types of questions on my own later.