- #1
tulsidas
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Homework Statement
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 AT.
We get,
AT A x = AT b
Solving for x now, we get
x = [inverse of ( AT A)] ATb
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?
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 AT on both sides from the left, is a valid one in the first place.
inverse of AT does not exist. So there is no way of returning back to the original system i.e Ax = b from AT A x = AT b
Is this a reasonable question and ,if not, where I am going wrong? What seems to be the problem?