Question: Please help me with this problem, thank you!!! Question 24. Let In be the n x n identity matrix. Let u be a unit vector

Please help me with this problem, thank you!!!

Question 24. Let In be the n x n identity matrix. Let u be a unit vector in R". Define Hn = In - 2uuf. Here a unit vector i means that norm |lull = 1 or equivalently wu = u . u = 1. (1) Is Hn an symmetric matrix? Prove your result. (2) Is Hn an orthogonal matrix? (i.e. is H, Hn = In?) (3) What is H2? (4) What is Hnu? . . . HE (5) Suppose u = in Write down H3 and HA

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