Answer
$u=\left(\dfrac{1}{5},\dfrac{3}{5}\right)$
$v=\left(\dfrac{1}{5},-\dfrac{2}{5}\right)$
Work Step by Step
We are given the system of equations:
$\begin{cases}
2u+3v=i\\
u-v=j
\end{cases}$
Solve the system:
$\begin{cases}
2u+3v=i\\
3u-3v=3j
\end{cases}$
$2u+3v+3u-3v=i+3j$
$5u=i+3j$
$u=\dfrac{i+3j}{5}=\dfrac{(1,0)+3(0,1)}{5}=\dfrac{(1,3)}{5}=\left(\dfrac{1}{5},\dfrac{3}{5}\right)$
$u-v=j$
$v=u-j=\left(\dfrac{1}{5},\dfrac{3}{5}\right)-(0,1)=\left(\dfrac{1}{5},-\dfrac{2}{5}\right)$
The solution is:
$u=\left(\dfrac{1}{5},\dfrac{3}{5}\right)$
$v=\left(\dfrac{1}{5},-\dfrac{2}{5}\right)$
