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

Now

and

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??

Thanks guys