sol-a10 - 2 2 = is { } 3 2 , u u , where = = 1 , 1 1 3 2 u...

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University of Toronto at Scarborough Department of Computer and Mathematical Sciences Linear algebra II MATB24 Fall 2008 Solution set to Assignment 10 Addition: The matrix representation of T with respect to the standard basis B = {1, x, x 2 } is = 3 0 1 1 2 1 2 0 0 B R The eigenvalues of T are 1 1 = λ and 2 2 = . The basis of eigenspace of R B corresponding to 1 1 = is { } 1 u , where ⎡− = 1 1 2 1 u . The basis of eigenspace of R B corresponding to
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Unformatted text preview: 2 2 = is { } 3 2 , u u , where = = 1 , 1 1 3 2 u u . The vectors 3 2 1 , , u u u are the coordinate vectors relative to B of p 1 (x) = - 2 + x + x 2 , p 2 (x) = - 1 + x 2 , p 3 (x) = x Therefore, {p 1 (x)} is a basis of and { p 2 (x), p 3 (x)} is a basis of . 1 E 2 E Fraleigh & Beauregard , 1...
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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-a10 - 2 2 = is { } 3 2 , u u , where = = 1 , 1 1 3 2 u...

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