B 0 Let A = [2 where B and C are block square matrices. a) If B and C are diagonalizable via Q and R (that is, Q-¹BQ and R-¹CR are diagonal), show that A is diagonalizable via Q 0 0 R where Q and R are block square matrices. X b) If x and y are eigenvectors of B and C, respectively, show that and are eigenvectors of A. 0 y

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