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Unformatted text preview: diagonalizable as it is a symmetric matrix. Apply GramSchmidt process to the set { (1 , 1 , 1) , (1 , 1 , 0) , (1 , , 1) } We will form an orthonormal set: • v 1 = (1 , 1 , 1) • v 2 = (1 , 1 , 0)proj v 1 (1 , 1 , 0) = (1 , 1 , 0) • v 3 = (1 , , 1)proj v 1 (1 , , 1)proj v 2 (1 , , 1) = (1 2 ,1 2 , 1) 1 •  v 1  = √ v 1 · v 1 = √ 3 ,  v 2  = √ v 2 · v 2 = √ 2 ,  v 3  = √ v 3 · v 3 = √ 6 • { ( 1 √ 3 , 1 √ 3 , 1 √ 3 ) , (1 √ 2 , 1 √ 2 , 0) , (1 √ 6 ,1 √ 6 , 2 √ 6 ) } is an orthonormal set. Form P : P = 1 √ 31 √ 21 √ 6 1 √ 3 1 √ 21 √ 6 1 √ 3 2 √ 6 Note that P1 = P T hence it is an orthogonal matrix. Find D : P1 AP = P T AP = D = 0 0 0 0 3 0 0 0 3 2...
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This document was uploaded on 04/26/2011.
 Spring '11

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