1 through 3 ask you to fill in some of the details of the analysis of the Lorenz equations in this section.(a) Show that the eigenvalues of the linear system (8), valid near the origin, are given byEq. (10).(b) Determine the corresponding eigenvectors.(c) Determine the eigenvalues and eigenvectors of the system (8) in the case where r = 28.
I I 1,1. \.i.Jl"'k /(;\h 1- \vi -J o,~ R.t-M.tM->~c,..l~tb c.)l(~ - ~ v"'Jv ~ - > I)\ t(. - ._ '\ ( Lll~X1,.l., - t•\t,o1,,loUJ(.ttJv~\-i~"'o~v.-,,.A.,.) 1\-I ) s: ." :~~ ~ ."' )1'1(~0~\(\ 1'1~ 1\')J.~