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Unformatted text preview: , based on the basis found. a) = , = + + : , , Math121A Sample Final Exam WQ10 4 b) g = GG , = { GG : = } . 7) Let : g be a linear transformation. a) Show that the null space of is a subspace of g . b) Show that the range of is a subspace of . Math121A Sample Final Exam WQ10 5 8) Let g: G () G () be the transformation g() = () () . Let = {2 + , 2 , 1 + } be a basis for G () . Find g . 9) Let g: be a linear transformation with the property that gg( ) = g( ) for every vector . a) Let be the range of g . In other words, = {g( )u } . If , then what is g( ) ? b) If , then what is g( g( )) ?...
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 Spring '08
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 Math

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