(10 pts) Let TV → V be a linear map and X1, ..., № be distinct eigenvalues of T with eigenspaces EX₁1, ..., Ex. Let W = E₁₁ + · + Exk (a) Show that W is a subspace of V. (b) Show that W = EX₁ = + Exk• λι (c) Show that if T is self-adjoint with respect to an inner product (,), then the direct sum W = Ex₁ ... Ek is an orthogonal decomposition, i.e., Ex, and Ex, are orthogonal with respect to (,) whenever λ¿ ‡ λ;.