Exercise 2.1.20

$P_1=\left[\begin{array}{cc}1\hfill & 0\hfill \\ 0\hfill & 0\hfill \end{array}\right]$projects onto the $x$-axis and $P_2=\left[\begin{array}{cc}0\hfill & 0\hfill \\ 0\hfill & 1\hfill \end{array}\right]$projects onto the $y$-axis. The vector $v=\left[\begin{array}{c}5\hfill \\ 7\hfill \end{array}\right]$ projects to $P_{1}v=\left[\begin{array}{c}5\hfill \\ 0\hfill \end{array}\right]$ and $P_2{P}_{1}v=\left[\begin{array}{c}0\hfill \\ 0\hfill \end{array}\right]$.