Question: 3. (a) Suppose V = U OW, where U and W are nonzero subspaces of V. Define P : V -> V by P(ut w)

3. (a) Suppose V = U OW, where U and W are nonzero subspaces of V. Define P : V -> V by P(ut w) = u, for every vectorl u + w E V. Find all eigenvalues and eigenvectors of P. (Note that P is what is known as a projection operator!) (b) Show that, for P as defined in (b), V = null(P) @ range(P). (c) True or false: for any linear operator T : V -> V, you can write V = null(T) @ range(T)

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