MATA23H3 Lecture Notes - Lecture 2: Linear Combination, Psa Tu Engine, Unit Vector

• School: UTSC
• Department: Mathematics
• Course: MATA23H3
• Professor: Chrysostomou( G)

Document Summary

Mata23 - lecture 2 - vectors in euclidian spaces continued. Geometric interpretation in r2: see diagram 1. (cid:126)v rn, (cid:126)v rn such that (cid:126)v + ( (cid:126)v) = (cid:126)0: r((cid:126)u + (cid:126)v) = r(cid:126)u + r(cid:126)v, aka distribution law . Further: (r + s)(cid:126)v = r(cid:126)v + s(cid:126)v, r(s(cid:126)v) = (rs)(cid:126)v, aka associative law , 1(cid:126)v = (cid:126)v, aka preservation of scalar , proof of #7: Let (cid:126)v = [v1, v2, , vn] rn. R, s r, r(s(cid:126)v) = [r(sv1), r(sv2), , r(svn)] |r: when r = 0, (cid:126)v = 0 (cid:126)w = (cid:126)0, when r = 1, (cid:126)v = (cid:126)w, see diagram 2. [9, 2, 7] = x1[1, 2, 1] + x2[6, 4, 2] = [1x1, 2x1, 1x1] + [6x2, 4x2, 2x2] = [x1 + 6x2, 2x1 + 4x2, x1 + 2x2] Solving for x1 and x2 we get x1 = 3, x2 = 2. X1(cid:126)u1 + x2(cid:126)u2 = 3[1, 2, 1] + 2[6, 4, 2]