Find the vector x R 3 that minimises abs(Ax-B)

where A = ([1 1 2], [1 2 1] ,[2 1 1] ,[2 2 1]) and b = (1 1 1 1) .

How do I solve the task using the normalvequation in python?

How to use scipy.optimize.fmin to solve the minimization problem

Im asked to replace b by b(a) = (1, a, 1, a)^T and plot the residual for each r(a) = abs(Ax(a) b(a)) versus a.

Does the curve have a zero? and if yes, what does this mean when solving over-determined linear systems?