[선형대수학-일차변환] Linear Mappings

Linear Mappings 1. Suppose the mapping $ F~:~R ^ {2} \rightarrow R ^ {2} $ is defined by $ F ( x,~y)= ( x+y,~x) $. Show that F is linear. pf) We need to show that $ F ( v+w)=F ( v)+F ( w) $ and $ F ( kv)=kF ( v) $, where $ v $ and $ w $ are any elements of $ R ^ {2} $ and $ k $ is any scalar. Let $ v= ( a,~b) $ and $ w= ( a ' ,~b ' ) $. Then $ v+w= ( a+a ' ,~b+b ' ) $ and $ kv= ( ka,~kb) $ We ha..

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