MATH 217 Study Guide - Quiz Guide: Scalar Multiplication, Linear Map
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Complete all work on this page, including the back, if needed. For each of the following collections of vectors in r3, decide. In the case of whether they are linearly dependent or linearly independent. linear dependence, give a non-trivial linear relation. (a) (b) (c) Let t : v w be a linear transformation. Prove that im(t ) is closed under addition and scalar multiplication. You may assume that v = rn and w = rm but you can earn extra credit if your proof also works for abstract vector spaces v , w . Let t : r2 r2 be rotation by 42 , and let s : r2 r2 be the orthogonal projection to the x-axis.