This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
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...
View
Full
Document
This note was uploaded on 12/20/2010 for the course MAT MATB24 taught by Professor X.jiang during the Spring '10 term at University of Toronto.
 Spring '10
 X.Jiang
 Linear Algebra, Algebra

Click to edit the document details