# Characteristic and Minimal polynomials of matrices

## Homework Statement

Let V=C^4 and consider the linear map V->V given by the matrix:

{{12,-6,6,-6},{2,21,21,51},{-3,12,12,30},{1,-9,-9,-21}}

(Each {...} denotes a row, tried to use Latex but got extremely confused!)

Given that chA(X)=(X-6)^4, calculate:

(i) The power such that mA(X)=(X-6)^b
(ii) A basis for the generalized eigenspace Vt(6) where t=1,...,b

## The Attempt at a Solution

I attempted to find b by sticking mA(A) into mathematica and seeing if there is a power such that mA(A)=0. This didn't work at all. Any help would be much appreciated.