Eigenvectors of Matrix: Solving Basics

[daveyman]

Homework Statement

Find the eigenvectors of the following matrix:

$$\[ \left( \begin{array}{ccc}<br /> 1 & 1 \\<br /> 4 & -2 \end{array} \right)\]$$

Homework Equations

N/A

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!

 

[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

 

[davyjones]

your sol'n times any c in R is fine

 

[daveyman]

your sol'n times any c in R is fine

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

Okay thanks!

 

[tshafer]

Exactly.

 

[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.