Let W be a T-invariant subspace of V. Let f(t), g(t) and h(t) be the characteristic polynomials of T, Tw and T , respectively. Prove that f(t) = g(t)h(t). Hint: use the fact that when you extend a basis y = {V₁, ... , Vk} for W to a basis ß = {V₁, ..., Vn} for V, that the images a = {Vk+1+W, ..., Vn+W} under the quotient map form a basis for V/W, and moreover, the matrix representation for [T] is block upper triangular of the form: [T] = [Tw]y [T]

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