- #1
icefall5
- 19
- 0
Homework Statement
The matrix [itex]A = \begin {bmatrix} 0 & -1 & 0 \\ 0 & -1 & 0 \\ 0 & 1 & 0 \end{bmatrix}[/itex] has two real eigenvalues, one of multiplicity 2 and one of multiplicity 1. Find the eigenvalues and a basis of each eigenspace.
Homework Equations
N/A
The Attempt at a Solution
I've done cofactor expansion to come up with the equation [itex] - \lambda^3 - \lambda^2[/itex], and that the eigenvalues are therefore -1 and 0, but I don't know how to determine the multiplicity of each. I've looked it up and have gotten nowhere. I can do the rest of the problem, I just don't know how to get these multiplicities.
EDIT: Working on the problem further, and I got the basis for -1. There are supposed to be two vectors for 0, however, but the RREF of the matrix is [itex]\begin{bmatrix} 0 & 1 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0 \end{bmatrix}[/itex]. How does that translate to two eigenvectors?
Thanks in advance for any help!
Last edited: