3
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The formula:

$A^T(b - Ax) = 0\\ A^Tb = A^TAx\\ x = (A^TA)^{-1}A^Tb$

What is the reason for multiplying both sides by the transpose of A?

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    $\begingroup$ Are you referring to the first equation? That is the least squares optimality condition. $\endgroup$ – Mark L. Stone Jun 23 '18 at 19:14
  • $\begingroup$ Yes, as Mark said you need to have complete derivation of the normal equation to get solution for beta - vector. $\endgroup$ – Analyst Jun 23 '18 at 19:39
  • $\begingroup$ I found the duplicates by searching; I know there are many more. $\endgroup$ – whuber Jun 23 '18 at 20:48