$A-4I= \left(\begin{array}{rrr} -3&2&0 \\ 2&-2&\sqrt2 \\ 0&\sqrt2&-3 \end{array}\right) $
From my calculations it seems that $x_1,x_2 \text{ and }x_3$ are all leading variables. However, my teacher expressed the basis in terms of $x_3$. What I know is that we can't express a basis in terms of leading variables, we can only in terms of free variables. Any help please?
The reduced form is: $\left(\begin{array}{rrr} 1&0&0 \\ 0&1&0 \\ 0&0&1 \end{array}\right) $
So all three are linearly independent, right?
How am I supposed to construct the eigenspace of this?