Answer
$$v=2 u_1-u_2.$$
Work Step by Step
Suppose the following linear combination
$$(4,4,5)=a(1,2,3)+b(-2,0,1)+c(1,0,0), \quad a,b,c\in R.$$
Which yields the following system of equations
\begin{align*}
a-2b+c&=4\\
2a&=4\\
3a+b&=5.
\end{align*}
Solving the above system, we get the solution $a=2$, $b=-1$, $c=0$. Hence,
$$v=2 u_1-u_2.$$
