# Quiz: Operations on Linear Mappings

### Question 1

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 $\mathit{M}\phantom{\rule{5px}{0ex}}:\phantom{\rule{5px}{0ex}}{ℝ}^{2}\phantom{\rule{5px}{0ex}}\to \phantom{\rule{5px}{0ex}}{ℝ}^{3}\mathit{}\phantom{\rule{3pt}{0ex}}$ be the linear mappings defined by $\mathit{L}\left(\mathit{x},\phantom{\rule{5px}{0ex}}\mathit{y}\right)\phantom{\rule{5px}{0ex}}=\phantom{\rule{5px}{0ex}}\left(4\mathit{x},\phantom{\rule{5px}{0ex}}\mathit{x}-3\mathit{y},\phantom{\rule{5px}{0ex}}-\mathit{y}\right)\phantom{\rule{3pt}{0ex}}$ and $\mathit{M}\left(\mathit{x},\mathit{y}\right)=\left(\mathit{x},\mathit{x},3\mathit{y}\right)\phantom{\rule{3pt}{0ex}}$. Calculate $\mathit{L}+\mathit{M}\phantom{\rule{3pt}{0ex}}$ and $5\mathit{L}\phantom{\rule{3pt}{0ex}}$.

$\left(\mathit{L}+\mathit{M}\right)\left(\mathit{x},\phantom{\rule{5px}{0ex}}\mathit{y}\right)\phantom{\rule{3pt}{0ex}}$ $=\phantom{\rule{3pt}{0ex}}$
 $\left(3x,3x-3y,5y\right)$ $\left(5x,3x-3y,3y\right)$ $\left(3x,5x-3y,2-3y\right)$ $\left(5x,2x-3y,3y\right)$ $\left(4x-3y,5x,3y\right)$

$\left(5\mathit{L}\right)\left(\mathit{x},\phantom{\rule{5px}{0ex}}\mathit{y}\right)\phantom{\rule{3pt}{0ex}}$ $=\phantom{\rule{3pt}{0ex}}$
 $\left(2-5y,20x-15y,5x\right)$ $\left(5x,20x-15y,-\left(5y\right)\right)$ $\left(20x,5x-15y,-\left(5y\right)\right)$ $\left(20x,20x-15y,5y\right)$ $\left(20y,5y-15x,-\left(5x\right)\right)$