Let $y=\left[\begin{array}{c}4\\ 9\\ 1\end{array}\right],u_1=\left[\begin{array}{c}\frac{1}{3}\\ \frac{2}{3}\\ \frac{2}{3}\end{array}\right],u_2=\left[\begin{array}{c}\frac{2}{3}\\ \frac{1}{3}\\ -\frac{2}{3}\end{array}\right],$ and $W=$ Span $\{u_1,u_2\}.$ Complete parts $($a$)$ and $($b$).$

a$.$ Let $U=\left[\begin{array}{cc}{u}_1& u_2\end{array}\right].$ Compute $U^{TT}U$ and $U{U}^{TT}.$

$U^{TT}U=,$ and $U{U}^{TT}=,($Simplify your answers.$)$