# Find eigen vectors and eigen spaces or $3 \times 3$ matrices

Hi I'm having trouble finding the eigenvectors of this matrix

$$\begin{bmatrix} 1 & -3 & 3\\ 3 & -5 & 3 \\ 6 & -6 & 4 \end{bmatrix}$$

I can't seem to simplify the matrix when I do the usual ($\lambda I-A$) calculation?

Also how can I find a basis for each eigen space?

• Have you found the eigenvalues? – Siong Thye Goh Aug 7 '17 at 21:52
• write a vector (a,b,c) and see for what values of $a,b,c$ there exists $\lambda$ such that $A(a,b,c)=\lambda(a,b,c)$ this is ugly 3 equations with 3 variables and 1 parameter.. – Yanko Aug 7 '17 at 21:53
• Hint: find $\lambda$ so $\det (A - \lambda I) = 0$. – Sean Roberson Aug 7 '17 at 21:55