Find the characteristic and minimal polynomials of(adsbygoogle = window.adsbygoogle || []).push({});

A=[[0,1,1][1,0,1][1,1,0]] (3x3 matrix)

So when I work out my characteristic polynomial I went

det(xI-A)= det[[x,1,1][1,x,1][1,1,x]]

= x(x^2-1)-1(x-1)+1(1-x)

= x^3-3x+2

= (x+2)(x-1)^2

It's odd because I worked this out several times, and by Cayley Hamilton's theorem it says that a characterstic polynomial of a matrix is also an annihilating polynomial for that matrix, and I tried plugging in A to the characteristic polynomial and it didn't give me the 0 matrix.

My prof's answer for the characteristic polynomial is (t-2)(t+1)^2

and her minimal polynomail is (t+1)(t-2)

Which works.

I'm really confused, can someone please tell me what I did wrong.

thanks in advance

**Physics Forums | Science Articles, Homework Help, Discussion**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Minimal and characteristic polynomial

**Physics Forums | Science Articles, Homework Help, Discussion**