Given the RCL circuit with a non-linear resistor where VR = R(i + i). The input is the voltage source V(t) and the output is the voltage over the capacitor Vc (t) Calculate part a) and b) manually with details. You can validate your answer with MATLAB. a) Find the mathematical state space model for the system b) Find the equilibrium point for a constant input voltage value V. c) Use ode45 command to compute, and plot the unit step response for L = 1, C = 0.5, R = 1. d) Find the equilibrium point for the input voltage v=10; and L=1, C= 0.5, R = 1; and find the linearized state space model for that equilibrium point. Given matrix A = 31 a) Find the eigenvalues and eigenvectors of A. b) Find the Diagonal form D of matrix A. c) Calculate eat with matrix Cayley-Hamilton theorem v() R i(t) C + Vect) L