Question:
How to find the eigenspace of $A$ corresponding to all the different real eigenvalues.
This matrix only three real eigenvalues, $\lambda = 5, 1, 1$. Step by step, how would I go about finding the eigenspace corresponding to an eigenvalue, say, $\lambda = 1$?
A = $\begin{bmatrix} 2 & 2 & -1\\ 1 & 3 & -1\\ -1 & -2 & 2\\ \end{bmatrix}$
Thanks!