From the unit vector $u=\left(\frac{1}{6},\frac{1}{6},\frac{3}6,\frac{5}6\right)$ construct the rank one projection matrix $P=uu^t.$
- a) Show that if $P=uu^t$ , then $u$ is an eigenvector with $\lambda=1$.
- b) If $v$ is perpendicular to $u$, show that $Pv=0$, then $\lambda=0$
- c) Find three independent eigenvectors of $P$ all with eigenvalue of $\lambda=0$.