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