Answer
$v$ can not be written as a linear combination of the vectors $u_1,u_2,u_3$.
Work Step by Step
Suppose the linear combination $v= au_1+bu_2+cu_3$, then we have
$$(-1,7,2)=a(1,3,5)+b(2,-1,3)+c(-3,2,-4), \quad a,b,c\in R.$$
Which yields the following system of equations
\begin{align*}
a+2b-3c&=-1\\
3a-b+2c&=7\\
5a+3b-4c&=2.
\end{align*}
One can see that the determinant of the coefficient matrix is zero and hence the system has no solution. , So $v$ can not be written as a linear combination of the vectors $u_1,u_2,u_3$.
