Question

4) Let {{-1,0,1},{0,2,0},{0,-3,1}} this is on a matric formate

4.1) Show that A is diagonalizable
4.2) Find an invertible matrix P and a diagonal
matrix D such that P^-1 AP=D
4.3) Calculate A^11

Answer 1

A is diagonalizable iff it has 3 linearly independent eigenvectors
so find the eigenvectors and verify that they are linearly independent

Answer 2

...for the next part, make a matrix \(P\) whose columns are the eigenvectors of \( A\)
then find \(P^{-1}\) and calculate \(P^{-1}AP\)
this should give you a diagonal matrix \(D\)

Answer 3

I presume there is a typo in your last question, so I don't know what to say about that part :P