Solution
= Solution
The <eigenspace> for 3 has <basis> $\{(1,1,1)^T\}$. The <eigenspace> for 0 is the plane $v_1+v_2+v_3=0$, with <basis>
$$
\boxed{E_3=\operatorname{span}\{(1,1,1)^T\},\qquad E_0=\operatorname{span}\{(1,0,-1)^T,(0,1,-1)^T\}.}
$$
The last two vectors are linearly independent and every vector in the plane equals $v_1(1,0,-1)^T+v_2(0,1,-1)^T$.