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I know how to do p5 basically, problem 7 is needed more important, Thanks src="/qa/attachment/10979164/" alt="Screen Shot 2019-12-10 at 11.50.26 PM.png" /> Attachment 1 Attachment 2 Attachment 3 ATTACHMENT PREVIEW Download attachment Screen Shot 2019-12-10 at 11.50.26 PM.png Problem 5. Consider the set of vectors {}}; ] and the vector y given by U1 1 0 1 73 = OHO = O (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. ATTACHMENT PREVIEW Download attachment Screen Shot 2019-12-10 at 11.50.50 PM.png 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. ATTACHMENT PREVIEW Download attachment Screen Shot 2019-12-10 at 11.51.10 PM.png (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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