Let V be the subspace of C[a,b] spanned by {1,ex,ex}, and let D be the differentiation operator on V .

6. Let V be the subspace of C[a,b] spanned by {1,em,e_m}, and let D be the differentiation operator on V. (a) Find the transition matrix P representing the change of coordinates from the ordered basis E : {1,e$,e_'\"} to the ordered basis H : {1,sinh(m),cosh(m)}. Recall that cosh(:c) : ex + e'x), sinh(:r) 2 ex ~ 833). (b) Find the matrix A = [D] H representing D with respect to the basis H. (c) Find the matrix B = [D] E representing D with respect to the basis E. d Verif that B : P'1 AP. ( y