MATH 241- Final Exam Guide - Comprehensive Notes for the exam ( 89 pages long!)
Document Summary
The study of linear algebra is about two basic things. We study vector spaces and structure preserving maps between vector spaces. A vector space is set v with two binary operations, addition and scalar multiplcation. A vector space will satisfy various distributive identities. A vector is a directed line segment corresponding to the displacement from points a to b (in r2). If a vector starts at the origin, we will say that the vector is in standard position. We can represent them as row vectors or column vectors depending on convenience. The zero vector (~0) is a special vector. ~v + ~0 = ~0 + ~v = ~v. ~v + ~w = hv1 + w1, v2 + w2i. ~v + ~w = h1 + 3, 2 + 4i = h4, 6i. Let c be a scalar and let ~v = hv1, v2 r2. c ~v = chv1, v2i = hcv1, cv2i. 2 h3, 4i = h2(3), 2(4)i = h6, 8i.
