MTH 341 Study Guide - Final Guide: Scalar Multiplication, Identity Matrix, Triangular Matrix
15 May 2019
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Directions: discuss and solve the following problems in your groups. You are encouraged to write out your work on additional pieces of paper. Keir , j , ea , the then then. It vector ) t vi ea . zero. Ji ( closed kill ea ( closed under under addition ) scalar multiplication (3) let ~u, ~w rn. Show that span{~u, ~w} is a subspace of rn. (this is an exercise in writing a simple proof. ) (4) let ~w r4. R4 : ~w ~u = 0. De nition: (modi ed from our book from page 204. ) Then the set of vectors {~b1,~b2, ,~bk} is a basis for v if the following two conditions hold. (a) span{~b1,~b2, ,~bk} = v (b) {~b1,~b2, ,~bk} is linearly independent. The the set of vectors {~e1, ~e2, , ~en} is the standard basis for rn.
