Answer
See solution
Work Step by Step
a) $U^TU=\begin{bmatrix}
1
\end{bmatrix}$
$UU^T=\begin{bmatrix}
\frac{1}{10}&\frac{-3}{10}\\\frac{-3}{10}&\frac{9}{10}
\end{bmatrix}$
b) $proj_Wy=\frac{y\cdot u_1}{u_1\cdot u_1}u_1=-2\sqrt{10}u_1=\begin{bmatrix}
-2\\6
\end{bmatrix}$
$(UU^T)y=\begin{bmatrix}
\frac{1}{10}&\frac{-3}{10}\\\frac{-3}{10}&\frac{9}{10}
\end{bmatrix}\begin{bmatrix}
7\\9
\end{bmatrix}=\begin{bmatrix}
-2\\6
\end{bmatrix}$
