Exercise 7.1.4

We have $A_1=\left[\begin{array}{cc}\hfill 1\hfill & \hfill 2\hfill \\ \hfill 3\hfill & \hfill -1\hfill \\ \hfill 2\hfill & \hfill 5\hfill \end{array}\right]$, and $b_1=\left[\begin{array}{c}\hfill -4\hfill \\ \hfill 1\hfill \\ \hfill -6\hfill \end{array}\right]$, so we have $A_1{v}_0+b_1=\left[\begin{array}{cc}\hfill 1\hfill & \hfill 2\hfill \\ \hfill 3\hfill & \hfill -1\hfill \\ \hfill 2\hfill & \hfill 5\hfill \end{array}\right]\left[\begin{array}{c}\hfill x\hfill \\ \hfill y\hfill \end{array}\right]+\left[\begin{array}{c}\hfill -4\hfill \\ \hfill 1\hfill \\ \hfill -6\hfill \end{array}\right]$.

If the output $w$is the sum of those three ReLU’s, we have $N=3$ and $m=2$, so $r(3,2)=3+3+1=7$ pieces in $w(x,y)$.