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Matrix Question:
Question 5 (a) Let S be akxk invertible symmetric matrix, and C be a kx k invertible matrix. Moreover, let a k-dimensional vector. Show the following equality be (b) Set 3 0 0 0 0 5 Calculate (CE)(CSC)-1 (Cr) and zTs-上 plain Does your answer contradict the claim in part (a)? Ex- Question 6 (a) Let X be an n x p matrix, and set S -xX. Suppose the spectral decomposition of S is s-ZZ1 λǐt i. Show that the p columns of Klub-. , tp] are pairwise orthogonal. (b) Let 3 2 -3-2 2 -3 Find a 2 x 2 orthogonal matrix P, such that the two column vectors of XP are perpendicular to each other

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