Consider the least squares problem Ax = b given by

(a) Write down the normal equations for this system. Your answer should be a a linear system with a single matrix and the vector of unknowns on the left hand side, and a single vector on the right hand side. Do this part manually.

(b) Factor A = QR, and then write down the resulting system Rx = QTb. Multiply QT and b so your answer so has a single matrix and the vector of unknowns on the left hand side, and a single vector on the right hand side. Do this part manually, but you may use a calculator on any difficult calculations. Also, you may use Matlab to check your work, but not to find the factoring.

(c) Solve the resulting systems from (a) and (b) and make sure you get the same result (or very nearly the same result there might be a small difference due to numerical error). You may use Matlab or a calculator on this part.

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