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I'm trying to find the Eigenvectors and eigenvalues of this matrix:

I get 0, 1, and -1 as my eigenvalues.

Starting with 0, I solve for reduced row echelon form and get the matrix:

My question is, and maybe my brain is just fried, but I'm confused at to what my vector should look like.

I know x3=0 and x4=0, but what about x1,2?

My guess: I would just assign them an arbitrary variable r?

For example

Another question: My characteristic equation is L^2(L^2-1)=0; Are my roots 0, 0, -1, 1 or 0, -1, 1?

Code:

```
[
0 0 0 0
0 0 0 0
0 0 0 1
0 0 1 0
]
```

I get 0, 1, and -1 as my eigenvalues.

Starting with 0, I solve for reduced row echelon form and get the matrix:

Code:

```
[
0 0 1 0 0
0 0 0 1 0
0 0 0 0 0
0 0 0 0 0
]
```

My question is, and maybe my brain is just fried, but I'm confused at to what my vector should look like.

I know x3=0 and x4=0, but what about x1,2?

My guess: I would just assign them an arbitrary variable r?

For example

**x**=<r,r,0,0>, let r=1, <1,1,0,0>?Another question: My characteristic equation is L^2(L^2-1)=0; Are my roots 0, 0, -1, 1 or 0, -1, 1?

Last edited: