Answer
${\bf{u}} = 2{\bf{v}} + 4{\bf{w}}$
Work Step by Step
We express ${\bf{u}}$ as a linear combination of ${\bf{v}}$ and ${\bf{w}}$:
${\bf{u}} = r{\bf{v}} + s{\bf{w}}$
$\left( {6, - 2} \right) = r\left( {1,1} \right) + s\left( {1, - 1} \right)$
Now we solve the system of equations:
$6=r+s$ ${\ \ }$ and ${\ \ }$ $-2=r-s$.
So, we have $r=6-s$. Substituting it in the equation $-2=r-s$ gives
$-2=6-2s$.
The solutions are $s=4$ and $r=2$.
Thus, ${\bf{u}} = 2{\bf{v}} + 4{\bf{w}}$.
