Hey Tweety.
Recall that the eigenvalues are the solutions to the characteristic equation which means they are the roots. Recall that if a polynomial has solutions a,b,c then we can factorize that polynomial as (x-a)(x-b)(x-c) = 0.
A is the matrix . You are given that A has eigenvalues -6 and 3, with algebaric multiplicities 1 and 2 respectively, and that the eigenspace .
a) use the given eigenvalues to find the characteristic equation of A. (do not expand det(A-ILAMBDA), but the construct the equation from its roots.
Hence use the hamilton theorem to find A^{-1} .
I dont know where to being. Any help appreciated,