## Elementary Linear Algebra 7th Edition

$$v=2 u_1-u_2+3u_3.$$
Suppose the following linear combination $$(3,0,-6)=a(1,-1,2)+b(2,4,-2)+c(1,2,-4), \quad a,b,c\in R.$$ Which yields the following system of equations \begin{align*} a+2b+c&=3\\ -a+4b+2c&=0\\ 2a-2b-4c&=-6. \end{align*} Solving the above system, we get the solution $a=2$, $b=-1$, $c=3$. Hence, $$v=2 u_1-u_2+3u_3.$$