In lecture #15 concerning projections and the method of least squares a really enjoyed the matrix approach to the problem - I have seem the same example in a 18.02 recitation, but the calculus approach does not seem to me so elegant as the 18.06 approach. I spot, however, a big shortcoming of the 18.06 style - we use geometric reasoning for the derivation and then simply state that our solutions holds for any dimension..but for higher dimensions our geometric interpretation no longer holds! Is there some kind of an equivalence principle? To bluntly put it - what works in R^3 works also in R^n?

Question