MAT223H1 Lecture Notes - Linear Map, Linear Independence
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Tutorial problems 3: let t : r3 r2 be a linear transformation such that t(cid:0) 2. (cid:1). (b) suppose that it is also true that t(cid:0) 0. 1 (c) find a 2 3 matrix a such that t (x) = ax for every x r3: let t : r3 r3 be a linear transformation de ned by t(cid:0) x1. Show that x2 x3 (cid:21) range(t ) (cid:54)= r3 by nding a vector that is not in the range. Explain why this means t is not 1-1 (nor onto): let t : rm rn be a linear transformation, and let {x1, x2, x3} be a linearly dependent set of vectors in rm. Prove that the set {t (x1), t (x2), t (x3)} is linearly dependent in rn: bonus let t : r2 r2 be de ned by.
