Answer
$\mathbf{v}=\mathbf{u}+\mathbf{w}$
Work Step by Step
Write $\mathbf{v}=(2,1)$ as a linear combination of $\mathbf{u}=(1,2)$ and $\mathbf{w}=(1,-1)$
If
$\mathbf{v}=a\mathbf{u}+b\mathbf{w}$
Then
$2=a+b$
$1=2a-b$
Adding these equations gives us
$3=3a\implies a=1$
Plugging this value back into our first equation gives us
$2=1+b\implies b=1$
And so our linear combination is simply just the sum
$\mathbf{v}=\mathbf{u}+\mathbf{w}$
