Linear Algebra

208 Chapter Three. Maps Between Spaces2.26 Let V, W, X be vector spaces with bases B, C, D.(a) Suppose that h: V → W is represented with respect to B, C by the matrix H.Give the matrix representing the scalar multiple rh (where r ∈ R) with respectto B, C by expressing it in terms of H.(b) Suppose that h, g: V → W are represented with respect to B, C by H and G.Give the matrix representing h + g with respect to B, C by expressing it in termsof H and G.(c) Suppose that h: V → W is represented with respect to B, C by H and g: W → Xis represented with respect to C, D by G. Give the matrix representing g ◦ hwith respect to B, D by expressing it in terms of H and G.