Answer
a=2, b=1 and c=-1
Therefore, V=2U1+U2-U3
Work Step by Step
Suppose the linear combination $v= au_1+bu_2+cu_3$, then we have
$$(0,5,-4,0)=a(1,3,2,1)+b(2,-2,-5,4)+c(2,-1,3,6), \quad a,b,c\in R.$$
Which yields the following system of equations
\begin{align*}
a+2b+2c&=2\\
3a-2b-c&=5\\
2a-5b+3c&=-4\\
a+4b+6c&=0.
\end{align*}
The augmented matrix is given by
$$\left[ \begin {array}{cccc} 1&2&2&2\\ 3&-2&-1&5
\\ 2&-5&3&-4\\ 1&4&6&0\end {array}
\right]
$$
Using Gauss-eleminition, we get
$$\left[ \begin {array}{cccc} 1&0&0&2\\ 0&1&0&1
\\ 0&0&1&-1
\\ 0&0&0&0\end {array} \right]
$$
a=2, b=1 and c=-1
Therefore, V=2U1+U2-U3
