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Unformatted text preview: 2 . a) Find B v T ) ( 1 , B v T ) ( 2 and B v T ) ( 3 . b) Find ) ( 1 v T , ) ( 2 v T and ) ( 3 v T . c) Find a formula for T ( a + a 1 x + a 2 x 2 ). d) Use the formula obtained in (c) to compute T ( 1+ x 2 ). 2) Let ) , , ( 3 2 1 u u u u = and ) , , ( 3 2 1 v v v v = . Determine which of the following are inner products on R 3 . For those that are not, list the axioms that do not hold. a) 3 3 2 2 1 1 4 2 , v u v u v u v u + + >= < b) 2 3 2 3 2 2 2 2 2 1 2 1 , v u v u v u v u + + >= < c) 3 3 2 2 1 1 , v u v u v u v u + >= < 1 3) Let and . Show that 4 4 2 = 4 3 2 1 u u u u U = 4 3 2 1 v v v v V 3 3 2 1 1 , v u v u v u v u V U + + + >= < is not an inner product on M 22 . 4) Let ) ( x p p = and ) ( x q q = be polynomials in P 2 . Show that ) 1 ( ) 1 ( ) 2 1 ( ) 2 1 ( ) ( ) ( , q p q p q p q p + + >= < is an inner product on P 2 . 2...
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 Spring '10
 X.Jiang
 Linear Algebra, Algebra

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