I know that depending on whether consistency condition is satisfied or not we get infinite or no solution. My understanding is that the case for which we have infinite solution are the least squares solution solving normal equation which has inverse of transpose(A)*A, but then if A is not invertible this also won't be invertible.
So how do we get solution in this case ?
I know by hand method in which we eliminate pivotal variables in terms of non pivotal variables and then we can set arbitrary values for non pivotal variables, hence getting infinite solutions.
I want to understand it from the perspective of arriving at the solution by solving normal equation.
So my main point of concern is that (A′A)^-1 = (A^-1)(A'^-1) = (A^-1)(A^-1)' which would require A to be invertible ?