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If W is a subspace of an inner product space V, and if {w1, W2, " . ., we} is an orthonormal basis of W, then given any r E Vdefine: k projw(x) = >(x, w;)wj, j=1 the orthogonal projection of x onto W. Let Tw : V - W be the linear transformation Tw(x) = projw (x). This Tw is called the orthogonal projection operator onto W. Part A. Show that Tu = Tw (where Tu means Two Tw). Part B. Explain why for all y e W, we have Tw(y) = y. Part C. Prove that 1 = max{| |Tw(x)| | : re V and | |x|| = 1}