# sol-a5 - , > < p p , where , >= < p p if and...

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University of Toronto at Scarborough Department of Computer and Mathematical Sciences Linear Programming and Optimazation MATB61 Winter 2008 Solution set to Assignment 5 Addition: 1) a) = 6 2 1 ) ( 1 B v T , = 2 0 3 ) ( 2 B v T , ⎡− = 4 5 1 ) ( 3 B v T . b) ) ( 1 v T = 16 + 51x + 19x 2 , ) ( 2 v T = – 6 – 5x + 5x 2 , ) ( 3 v T = 7 + 40x + 15x 2 . c) T ( a 0 + a 1 x + a 2 x 2 ) = 2 2 1 0 2 1 0 2 1 0 12 107 31 61 8 247 111 201 24 289 161 239 x a a a x a a a a a a + + + + + d) T ( 1+ x 2 ) = 22 + 56x + 14x 2 2) a)Yes. b) No. Axioms 2 and 3 fail. c) No. Axiom 4 fail. 3) Axiom 4 fail. Let and be nonzero matrices but = 0 1 0 0 U = 0 0 1 0 V 0 , >= < V U . Or, Let be nonzero matrices but = 0 1 1 0 U 0 2 , >= < U U . 4) Verify the axioms P1 – P3. P4:

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Unformatted text preview: , > < p p , where , >= < p p if and only if = p . Its easy to see that ) 1 ( ) 2 1 ( ) ( ) 1 ( ) 1 ( ) 2 1 ( ) 2 1 ( ) ( ) ( , 2 2 2 + + = + + >= < p p p p p p p p p p p . If = p , i.e. p(x) = 0, then , >= < p p . 1 On the other hand, if , >= < p p , we have ) 1 ( , ) 2 1 ( , ) ( = = = p p p . Since p P 2 , let p(x) = ax 2 + bx + c and plug 0, and 1 into it to obtain 3 equations: c = 0 a + b + c = 0 a + b + c = 0 Solve the equations to obtain a = b = c = 0 . Therefore ) ( = = x p p . Fraleigh & Beauregard , 2...
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## 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- Toronto.

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sol-a5 - , > < p p , where , >= < p p if and...

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