Sorry if the title isn't very descriptive. However, I've seen the following problem while I'm solving linear problems
Write down $E=||Ax-b||^2$ as a sum of four squares - the last one is $(C+4D-20)^2$. Find the derivative equations $\partial E/\partial C=0$ and $\partial E/\partial D=0$. Divide by $2$ to obtain the normal equations $A^TA\hat{x}=A^Tb$.
with the given solution
Observe $$A=\begin{pmatrix}1 &0\\1 &1\\1 &3\\1 &4\\\end{pmatrix}\text{, }b=\begin{pmatrix}0\\8\\8\\20\end{pmatrix}\text{ , and define }x=\begin{pmatrix}C\\D\end{pmatrix}$$
$$Ax-b=\begin{pmatrix}C\\C+D-8\\C + 3D − 8\\C + 4D − 20\\\end{pmatrix}\text{, }$$
$||Ax − b||^2 = C^2 + (C + D − 8)^2 + (C + 3D − 8)^2 + (C + 4D − 20)^2$ .
Where do the values of the matrix A come from? I don't find any relative thing in the question. Thanks.