QUESTION 4 (a) Let A be an m _m symmetric matrix and P be an orthogonal matrix such the PAP-D,where D is a diagonal matrix with the characteristic roots of A on the diagonal. Show that PA P is also a diagonal matrix. (b) Let A be an m _n matrix of rank m such that A = BC where B and C each has rank m. Show that (BC) CB. 16 STA4801/101/0/2019 (c) For the matrix A find a c-inverse. -1 0
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