The following system of equations is designed to determine the concentrations $($c$\text{'}$s in $\frac{g}{m^3})$ in a series of coupled reactors as a function of the

amount of mass input into each reactor $($right hand sides$)$ in g$/$day$.$

$15c_1-3c_2-c_3=3800$

$-3c_1+18c_2-6c_3=1200$

$-4c_1-c_2+12c_3=1350$

a$)$ Using LU functions in Matlab, determine the values of c$\text{'}$s that will solve the system. Call this column vector C$.$ Note: you should use Matlab's

built$-$in $)$ function here, no need to calculate $L$ and $U$ by hand. Then, solve $Ly=b$ for $y,$ where $b$ is the right$-$side vector, followed by $UC=y$ for

C$.$

b$)$ Next determine how much the rate of mass of reactor $3$ must be increased to induce at least a $10\frac{g}{m^3}$ rise in the concentration of reactor $1.$ Do

this by progressively increasing the mass of reactor $3$ in increments of $1\frac{g}{?}$ day until the concentration of reactor $1$ is above the desired level. Call

your new $b$ vector B$2.$ For this part it is fine to use either LU or slash.