(Solved): Linearize these two nonlinear equations for a jacketed CSTR with an irreversible \( A \rightarrow ...

Linearize these two nonlinear equations for a jacketed CSTR with an irreversible \( A \rightarrow B \) reaction and find the six transfer functions . There should be two transfer functions for each input variable (Tf, Tj, CAf) that affect the two output variables which are CA and \( T \). Show all the steps please. \[ \begin{aligned} \frac{d C_{A}}{d t} &=\frac{F}{V}\left(C_{A_{f}}-C_{A}\right)-r=f_{1}\left(C_{A}, T\right) \\ \frac{d T}{d t} &=\frac{F}{V}\left(T_{f}-T\right)-\left(\frac{\Delta H}{C_{p} \rho}\right) T-\frac{U A}{C_{p} \rho V}\left(T-T_{j}\right)=f_{2}\left(C_{A}, T\right) \\ r &=k_{o} \exp \left(\frac{-\Delta E}{R T}\right) C_{A} \end{aligned} \] Constants: Volume \( (\mathrm{V}) \), flow rate \( (\mathrm{F}) \), heat capacity \( \mathrm{Cp} \), density, overall heat transfer coefficient \( (U) \), heat transfer area \( (A) \), and heat of reaction ( \( \Delta H r) \)