Are Both Eigenvectors Correct?

[Cpt Qwark]

say for example when I calculate an eigenvector for a particular eigenvalue and get something like
$$\begin{bmatrix}<br /> 1\\<br /> \frac{1}{3}<br /> \end{bmatrix}$$

but the answers on the book are

$$\begin{bmatrix}<br /> 3\\<br /> 1<br /> \end{bmatrix}$$

Would my answers still be considered correct?

 

[Kyouran]

Yes, multiplying an eigenvector with a scalar yields another eigenvector (makes kind of sense right? Think about the definition). Usually people will multiply the result with whatever scalar makes all the entries integers for representation purposes, but both results are correct.