Exercise 4.4.21

The orthonormal vectors are $q_1=(1,1,1,1)∕2$ and $q_2=(-5,-1,1,5)∕\sqrt{52}$. Then $b=(-4,-3,3,0)$ projects to $p=\left(q_1^{T}b\right)q_1+\left(q_2^{T}b\right)q_2=(-7,-3,-1,3)∕2$. And $b-p=(-1,-3,7,-3)∕2$ is orthogonal to both $q_1$ and $q_2$.