Assignment 17

# Assignment 17 - 29 29 1 max max C t a b t a b x x x x t x t...

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Math 225 Spring 2008 Rosen Assignment 17 1. Show that { } , n R R is a Normed Linear Space. 2. Show that [ ] { } , , p C a b with 1 p = and p = are Normed Linear Spaces. 3. For n n A R R R let ( 29 , 1 max n i j i j N A a = = (i.e. the maximum absolute row sum of A) and let : n n F R R R be given by ( 29 F x Ax = r r for n x R R r , Show that ( 29 ( 29 ( 29 F x F y N A x y R R - - r r r r for , n x y R R r r . Conclude that : n n F R R R is continuous from { } , n R R into { } , n R R . 4. For [ ] 1 , x C a b R let
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Unformatted text preview: [ ] ( 29 [ ] ( 29 1 , , max max C t a b t a b x x x x t x t R & = + = + . Show that [ ] { } 1 1 , , C C a b is a Normed Linear Space. Let [ ] [ ] 1 : , , F C a b C a b R given by ( 29 F x xR = for [ ] 1 , x C a b R is continuous from [ ] { } 1 1 , , C C a b into [ ] { } , , C a b R...
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