Exercise 4.4.31

(a) $c=\frac{1}{2}$ normalizes all the orthogonal columns to have unit length

(b) The projection $\left(a^{T}b∕a^{T}a\right)a$ of $b=(1,1,1,1)$ onto the first column is $p_1=\frac{1}{2}(-1,1,1,1)$. (Check $e=0$.) To project onto the plane, add $p_2=\frac{1}{2}(1,-1,1,1)$ to get $(0,0,1,1)$.