Question: 3. (30 pts) (a) Define a transformation P: Man - Man by P(A) = A - AT for all A in Man. (a) (5 pts)

3. (30 pts) (a) Define a transformation P: Man - Man by P(A) = A - AT for all A in Man. (a) (5 pts) Show that P is linear. (b) (10 pts) Identify im(P), then find basis for that. (c) (10 pts) Identify ker(P), then find basis for that. (d) (5 pts) Let U and V denote the spaces of n x n symmetric and skew-symmetric matrices, respectively. Show that dimU + dimV = n2

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