Row Reduction & Rank · Hard problem

A $3$-sector economy has consumption matrix $C=\begin{pmatrix}0.1&0.2&0.3\\0.3&0.1&0.2\\0.2&0.3&0.1\end{pmatrix}$ (the fraction of each sector's output consumed by other sectors) and faces external demand $\mathbf d=(56,30,10)$. The production vector $\mathbf x$ satisfying $(I-C)\mathbf x=\mathbf d$ tells each sector how much it must produce in total. Find $x_1$, sector $1$'s required output.