Recent content by muzziMsyed21

Homework Statement Prove that if A is an nxn matrix with eigenvector v, then v is an eigenvector for Ak where kε(all positive integers) Homework Equations Av=λv The Attempt at a Solution Av=λv A(Av)=A(λv) Akv=λ(Av) i know i may not be doing it right but this is what i can...

Homework Statement Let A and C be nxn matrices with C invertible. Prove that A and C-1AC have the same eigenvalues. Homework Equations B=C-1AC The Attempt at a Solution det(A-λI) =det(B-λI) det(A-λI) =det(C-1AC - λI) det(A-λI) =det(C-1AC - λC-1IC) det(A-λI) =det[CC-1(A-λI)]...

does it have anything to do with additive inverse?

det(AT)=det(-A) det(A)=(-1)ndetA from here i still don't know how det=0

kndet(A)

that is where i am stumped... is it det(A) = -det(A) then detA=0 ?

sorry for the typos I edited and fixed them

Homework Statement Let A and P be square matrices of the same size with P invertible, Prove detA=det(P-1AP) Homework Equations Suppose that A and B are square matrices of the same size. Then det(AB)=det(A)det(B) The Attempt at a Solution detA=det(P-1AP) detA=det(P-1PA) detA=det(IA)...