Answer
$\mathbf{v}=\mathbf{u}+2\mathbf{w}$
Work Step by Step
Write the vector $\mathbf{v}=(3,0)$ as a linear combination of $\mathbf{u}=(1,2)$ and $\mathbf{w}=(1,-1)$
If
$\mathbf{v}=a\mathbf{u}+b\mathbf{w}$
Then
$3=a+b$
$0=2a-b$
If we add these equations together we get
$3=3a\implies a=1$
Substituting this value back into our first equation gives us
$3=1+b\implies b=2$
This is consistent with our second equation:
0=2-2
So our linear combination is
$\mathbf{v}=\mathbf{u}+2\mathbf{w}$