MATA23H3 Lecture Notes - Lecture 14: Scilab, Linear Map
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T ((cid:126)u) + t ((cid:126)v) = t ( , (cid:126)v = (u1 + v1) (cid:21) (cid:20)v1 (cid:21) (cid:20)u1 v2. 4(u1 + v1) 2(u2 + v2) (cid:20)u1 (cid:21) (cid:21) (cid:20)v1. 2(u1 + v1) + 3(u2 + v2) (cid:20)u1 (cid:21) 2u1 + 3u2 + 2v1 + 3v2 (cid:20)ru1 (cid:20)u1 (cid:21) T (r(cid:126)u) = t (r (cid:21) (cid:20)v1 v2 (cid:21) Mata23 - lecture 14 - properties of linear transformations. Properties of linear transformations: example 1: determine whether t : r2 r3 de ned by t ( (cid:20)x1 (cid:21) x2. T ((cid:126)u + (cid:126)v) = t ( ) = t ( u2 v2 (cid:20)u1 + v1 u2 + v2 (cid:21) T is a linear transformation: let t be a linear transformation from rn rm. Then: t ((cid:126)0) = (cid:126)0 (cid:126)0 is domain, (cid:126)0 codomain, t ( (cid:126)u + (cid:126)v) = t ((cid:126)u) + t ((cid:126)v) 1: more generally, if (cid:126)v1, (cid:126)v2, . , (cid:126)vk are vectors in rn and c1, c2, .
