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sol-assignment11 - B corresponding to 2 2 is 3 2 u u where...

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1 University of Toronto at Scarborough Department of Computer and Mathematical Sciences Linear algebra II MATB24 Fall 2010 Section 7.2
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3 Section 8.1
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6 Section 8.2
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9 4. 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 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
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Unformatted text preview: B corresponding to 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 1 E and { p 2 (x), p 3 (x)} is a basis of 2 E ....
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