- #1
cateater2000
- 35
- 0
Find the characteristic and minimal polynomials of
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
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