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I know how to do p5 basically, problem 7 is needed more important, Thanks

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Problem 5.
Consider the set of vectors {}}; ] and the vector y given by
73 =
(a) If w = E_cju; for some coefficients {c;) , give the system of linear equations (in
matrix form) that express the condition wi = yi for i = 1, ...4.
(b) Give the normal equations (in matrix form) that need to be solved to determine
the coefficients {cj} _, so that ||w - y'll2 is minimized.

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Problem 7.
Still consider the least squares approximation problem in Problem 5:
(a) If the matrix of the system in Problem 5 (a) is V, use Householer transformation
to find the QR factorization of V.

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(b) Use above Householder QR factorization of V to build the system for solving the
linear equations in Problem 5 (a) so that “117 — 37l|2 is minimized. (c) Solve the system you build in Problem 7 (b) using back substitution to determine
the values of the coefficients {cj L1.

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