Question: Let A be an n n matrix and let B = A + AT and C = A - AT (a) Show that B

Let A be an n × n matrix and let
B = A + AT and C = A - AT
(a) Show that B is symmetric and C is skew-symmetric.
(b) Show that every n × n matrix can be represented as a sum of a symmetric matrix and a skew-symmetric matrix.

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