Answer
See explanation
Work Step by Step
$W=\left[\begin{array}{ll}X & x_{0}\end{array}\right]$
Get factor $W W^{T}$ :
$W^{T} W=\left[\begin{array}{c}X^{T} \\ x_{0}^{T}\end{array}\right] \cdot\left[\begin{array}{ll}X & x_{0}\end{array}\right]=\left[\begin{array}{cc}X^{T} X & X^{T} x_{0} \\ x_{0}^{T} X & x_{0}^{T} x_{0}\end{array}\right]$
Use formula for $S$ from Exercise 15 :
$S=x_{0}^{T} x_{0}-x_{0}^{T} X\left(X^{T} X\right)^{-1} X^{T} x_{0}$
$=x_{0}^{T}\left(I_{m}-X\left(X^{T} X\right)^{-1} X^{T}\right) x_{0}$
$=x_{0}^{T} M x_{0}$
