Let l3 = {bJ. b2 .. ". b,} be a basis for n". lllld let
Chapter , Problem 98(choose chapter or problem)
Let l3 = {bJ. b2 .. ". b,} be a basis for n". lllld let c1. c2, . .. c., be (not necessarily distinct) vectors in n. (a) Show that the matrix transfonnation T induced by cs-1 satisfies T(bJ) = CJ for j = 1,2, ... . n. (b) Prove that the linear transformation in (a) is the unique linear transformation such that T(bJ) = CJ for j = 1.2 ..... 11. (c) Extend these results to an arbitrary linear transformationT :'R"~nm
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