The following separation system is given:$-$

We are interested in calculating the unknown mass flow rates of each outlet stream. Each streams consisting of various chemical based components $w_1,w_2$ and $w_3.$ You may define the

a$)$ Mass balances for total flow rates and components balances for at least two components. Solve the linear algebraic equations using numerical method.

$(4\mathrm{.}5$ marks$)$

b$)$ Apply MATLAB and solve the linear algebraic equations attained from part $($a$)$ using Crout Lower$-$upper $($LU$)$ decomposition method.

$(3$ marks$)$