Hi just a quickish question: Show that the least squares solution of (where x and b are column vectors) is not unique and solve the normal equations to find all the least squares solutions.
My solution: The least squares solution will not be unique since the columns of A are not linearly independent.(by least squares theorem)
i.e. we can find scalars such that
ok so i went through with this and found where t is a free variable
The normal equations are given by
when i solved this i got where r is a free variable
So this is the least squares approximation??