The Jacobian. Consider the nonlinear systemShow that (−1/3,4/3) is an equilibrium point of...

The Jacobian. Consider the nonlinear system

Show that (−1/3,4/3) is an equilibrium point of the system.

a) Without the use of technology, calculate the Jacobian of the system at the equilibrium point (−1/3, 4/3). What is the equation of the linearization at this equilibrium point? Use [v,e]=eig(J) to find the eigenvalues and eigenvectors of this Jacobian.

b) Enter the system in pplane6. Find the equilibrium point at (−1/3,4/3). Does the data in the Equilibrium point data window agree with your findings in part (a)? Note: The eigenvalues of the Jacobian predict classification of the equilibrium point. In this case, the point (−1/3,4/3) is a saddle because the eigenvalues are real and opposite in sign.

c) Display the linearization. Does the equation of the linearization agree with your findings in part (a)?