# Quiz: Operations on Linear Mappings

### Question 2

1 point

Let $\mathit{L}\phantom{\rule{5px}{0ex}}:\phantom{\rule{5px}{0ex}}{ℝ}^{2}\phantom{\rule{5px}{0ex}}\to \phantom{\rule{5px}{0ex}}{ℝ}^{3}\mathit{}\phantom{\rule{3pt}{0ex}}$ and $\mathit{M}\phantom{\rule{5px}{0ex}}:\phantom{\rule{5px}{0ex}}{ℝ}^{3}\phantom{\rule{5px}{0ex}}\to \phantom{\rule{5px}{0ex}}ℝ\phantom{\rule{3pt}{0ex}}$ be the linear mappings defined by $\mathit{L}\left(\mathit{x},\phantom{\rule{5px}{0ex}}\mathit{y}\right)\phantom{\rule{5px}{0ex}}=\phantom{\rule{5px}{0ex}}\left(2\mathit{x}+\mathit{y},\phantom{\rule{5px}{0ex}}0,\phantom{\rule{5px}{0ex}}\mathit{x}-5\mathit{y}\right)\phantom{\rule{3pt}{0ex}}$ and $\mathit{M}\left(\mathit{x},\mathit{y},\mathit{z}\right)=\mathit{x}+3\mathit{y}-5\mathit{z}\phantom{\rule{3pt}{0ex}}$. Calculate $\mathit{M}\circ \mathit{L}\phantom{\rule{3pt}{0ex}}$.

 $\left(\mathit{M}\circ \mathit{L}\right)\left(\mathit{x},\phantom{\rule{5px}{0ex}}\mathit{y}\right)\phantom{\rule{3pt}{0ex}}$ $=\phantom{\rule{3pt}{0ex}}$