assignment5 - 2 . a) Find B v T ) ( 1 , B v T ) ( 2 and B v...

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University of Toronto at Scarborough Department of Computer and Mathematical Sciences Linear Algebra II MATB24 Fall 2008 Assignment # 5 You are expected to work on this assignment prior to your tutorial in the week of October 13th, 2008. You may ask questions about this assignment in that tutorial. In your tutorial in the week of October 20th you will be asked to write a quiz based on this assignment and/or related material from the lectures and tutorials in week 5 and textbook readings. Textbook: Linear Algebra by Fraleigh & Beauregard, 3rd edition. Read: Chapter 3 Section 4, 5 and Lecture 5 Notes Problems: 1. , Pages 226 - 228 # 16, 17, 18, 20, 21, 22, 24, 25, 26, 28, 29, 31, 32, 48 2. , Pages # 1, 2, 5, 6, 7, 8, 11, 12, 13 3. Addition: 1) Let be the matrix of T: P 2 P 2 with respect to the basis = 4 2 6 5 0 2 1 3 1 A {} 3 2 , where 1 , , v v v B = 1 v = 3x + 3x 2 , 2 v = - 1 + 3x + 2x 2 , 3 v = 3 + 7x + 2x
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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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assignment5 - 2 . a) Find B v T ) ( 1 , B v T ) ( 2 and B v...

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