Overdetermined system: You're running a continuous culture of $E.$ coli in the lab.

$3$ substrates: glycerol $(C{H}_{\frac{8}{3}}O),O_2,N{H}_3$

$2$ products: $C{O}_2$ and $H_{2}O$

Biomass composition: $C{H}_{2\mathrm{.}3}{O}_{0\mathrm{.}5}{N}_{0\mathrm{.}25}$

In the culture, you measure the rates $(C-$mol$\frac{i}{C}-$molx$-h)$ for glycerol, oxygen, and biomass, as shown in the vector below.

$r_m=([],[r_{gly}],[r_{O2}])=([0\mathrm{.}5],[-0\mathrm{.}75],[-0\mathrm{.}03])$

Be sure to show your code and your output.

b$.$ Set up matrices $E_f$ and $E_m.$

c$.$ Solve for $r_s$

c$.$ Solve for $$ and $F.$ The error in the rate for each component is $5\%$

d$.$ Solve for $R$ and $R_r.$

e$.$ Solve for epsilon and $P.$

f$.$ Solve for hat$()$ and hat$(r{)}_m.$ How do your estimated rates compare to your measured rates given in the problem statement?

g$.$ Use the test function h to evaluate errors in the data. What can you conclude about the quality of the data?