# Homework Help: Eigenvector Basics

1. Nov 24, 2008

### daveyman

1. The problem statement, all variables and given/known data

Find the eigenvectors of the following matrix:

$$$\left( \begin{array}{ccc} 1 & 1 \\ 4 & -2 \end{array} \right)$$$

2. Relevant equations

N/A

3. The attempt at a solution

I already know how to find the solutions. They are {1 1} and {-1 4}. My question is this: could a solution also be {1 -4} (switching the minus sign)? I don't think it is a solution but I don't see why not...

Any help would be great. Thanks!

2. Nov 24, 2008

### tshafer

Have you tried $$\begin{pmatrix}1 \\ -4\end{pmatrix}$$ ? All it takes to be a solution is solving the eigenvalue problem for some eigenvalue $$\lambda$$.

Tom

3. Nov 24, 2008

### davyjones

your sol'n times any c in R is fine

4. Nov 24, 2008

### daveyman

Oh I guess that's obvious huh. So if c=-1, I'm good.

Okay thanks!

5. Nov 24, 2008

### tshafer

Exactly.

6. Nov 24, 2008

### HallsofIvy

One important thing you should have learned (or maybe this exercise is in preparation) the set of all eigenvectors (corresponding to a given eigenvalue) forms a subspace: it is closed under both vector addition and scalar multiplication.