a$)$ Return to the controller canonical form state representation $($A$,$ B$,$ C$)$ you obtained in

Workshop $6.$ Find the eigenvalues and eigenvectors of the matrix A$,$ showing all the

necessary steps in your calculations.

NOTE: For ease of marking, while computing the eigenvectors, please set the first $($top$)$

nonzero element of the intermediate vectors to $1.$ Since you need the values of these

vectors for the further comparison with the MATLAB values, present all the numbers

in the decimal format.

$1$

$($b$)$ i$.$ Obtain a coordinate transformation $$x $=$ P x that will give an equivalent diagonal

state representation $($A$,$B$,$C$)$ for the rabbit population system. Also give the

matrices $$A$,$B and $$C$.$

ii$.$ Why is the diagonal representation useful?