Let g(t) be the auxiliary polynomial associated with a homogeneous linear differential equation with constant coefficients (as defined in Section 2.7), and let V denote the solution space of this differential equation. Prove the following results. (a) V is a D-invariant subspace, where D is the differentiation operator on C. (b) The minimal polynomial of Dv (the restriction of D to V) is g(t). (c) If the degree of g(t) is n, then the characteristic polynomial of Dv is(-l)n g(t). Hint: Use Theorem 2.32 (p. 135) for (b) and (c).

AP English: Literature and Composition Name: Emily Armogan Major Works Data Sheet Biographical information about the author: Title: Pygmalion Author: George Bernard Shaw George Bernard Shaw was born July 26 , 1856 in Dublin, Ireland. His mother was a singer and his Date of Publication: 1941 father was a merchant. He developed over 60 plays devoted to criticism. He was married to Charlotte Genre: Romantic Comedy, Social Criticism Payne Townsend for 45 years till her death in Historical information about the period of publication:43.