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Let P: R 3 → R 3 be the projection onto the plane x + y − z = 0.
a) Prove that P is linear. 
b) Prove that P o P = P. 
c) Find bases for the subspaces Null(P) and Range(P). 
d) Find the standard matrix A of P and show that A^2 = A and A = A^T.