- #1
Neoon
- 25
- 0
Hi
I came across a problem of eigenvalues and eigenvectors. It was easy and I solved it but one thing made me unsure about the answer. All the three eigenvectors were zero vectors. Here is the question and my answer:
The matrix A=
( -1 0 0 1
0 -2 0 0
0 1 -2 0
0 0 0 1)
I began with finding the eigenvalues. The result is the following fourth order equation (x=lamda=eigenvalue):
x^4+4x^3+x^2-6x-4=0
When i solved this equation using Texas Instruments calculator, it found three solutions:
x1=-(sqrt(5)+1)
x2=(sqrt(5)-1)
x3= -1
x4= -1
So, I had three eignevectors because x3=x4=-1 (multiplicity 2)
When I used these eigenvalues to find the eigenvectors, all of the eigenvectors turned out to be=
(0
0
0
0)
My question: is this reasonable solution to have all of the eigenvectors= 0 or I have made a mistake somewhere.
Thanks in advance
I came across a problem of eigenvalues and eigenvectors. It was easy and I solved it but one thing made me unsure about the answer. All the three eigenvectors were zero vectors. Here is the question and my answer:
The matrix A=
( -1 0 0 1
0 -2 0 0
0 1 -2 0
0 0 0 1)
I began with finding the eigenvalues. The result is the following fourth order equation (x=lamda=eigenvalue):
x^4+4x^3+x^2-6x-4=0
When i solved this equation using Texas Instruments calculator, it found three solutions:
x1=-(sqrt(5)+1)
x2=(sqrt(5)-1)
x3= -1
x4= -1
So, I had three eignevectors because x3=x4=-1 (multiplicity 2)
When I used these eigenvalues to find the eigenvectors, all of the eigenvectors turned out to be=
(0
0
0
0)
My question: is this reasonable solution to have all of the eigenvectors= 0 or I have made a mistake somewhere.
Thanks in advance