Exercise 4.3.3

In Problem 2, $p=A{\left(A^{T}A\right)}^{-1}{A}^{T}b=(1,5,13,17)$ and $e=b-p=(-1,3,-5,3)$.

This $e$ is perpendicular to both columns of $A$. This shortest distance $\parallel e\parallel$ is $\sqrt{44}$.