MAT224H1 Lecture Notes - Lecture 9: Surjective Function, Injective Function, If And Only If
Document Summary
T is surjective iff dim imu dim v dim w butwww. iiiij. ihidimw tsurjective anti w. If dim we dimv thereis no injective t e ic v w. If dim a dim w thereis no surjective tel cv w dimv dim kerlt t dim imu dimw. 30 dimw dimlimct egt x1 x 2 x3 dd_ pm ir. Thmy suppose dim w dim v t o injective iff it"s surjective. A t c lcv w is a dim kerli. 2 suppose t is surjective but dim limit dim her t dim kevlt dim w dim u. 17m dim u can t be dim v surg ing x dimv a dim w can t be surg x ing v. 4hm t e l v w bet we im t. Then v uz et and the compositionis unique w. Them is t w a subspace sometimes is subspace iff w. O to w w w is a subspace then oet.
