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