Exercise 4.3.30

When $A$ has orthogonal columns $(1,\dots ,1)$ and $\left(T_1,\dots ,T_m\right)$, the matrix $A^{T}A$ is diagonal with entries $m$ and $T_1^2+\cdots +T_m^2$. Also $A^{T}b$ has entries $b_1+\cdots +b_m$ and $T_1{b}_1+\cdots +T_m{b}_m$. The solution with that diagonal $A^{T}A$ is just the given $\hat{x}=(C,D)$.