(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

The system Ax = b does not have a solution.

A is a full column rank matrix.

Multiply both sides of the equation, Ax =b with A^{T}.

We get,

A^{T}A x = A^{T}b

Solving for x now, we get

x = [inverse of ( A^{T}A)] A^{T}b

By using relevant examples, we find that solution for the system exists, a contradiction to what the system looked like originally!

How is this possible? Is there some incorrect assumption?

3. The attempt at a solution

One doubt that I have is that I am not entirely sure whether the operation of multiplying the system with A^{T}on both sides from the left, is a valid one in the first place.

inverse of A^{T}does not exist. So there is no way of returning back to the original system i.e Ax = b from A^{T }A x = A^{T}b

Is this a reasonable question and ,if not, where I am going wrong? What seems to be the problem?

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# Homework Help: Question on Linear Algebra

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