Unformatted text preview: [1] (4) Let A = 13 3 35 3 66 4 . Find the eigenvalues of A and a basis for each of the associated eigenspaces. [4] (5) Diagonalize the following matrix. 21 2 3 2 [4] (6) Let the sequence a , a 1 , a 2 , ··· be given by a = 0 , a 1 = 1 , and a k = ( a k1 + a k2 ) / 2 for k ≥ 2 . Find the matrix that can be used to generate this sequence as we used a matrix to generate the Fibonacci sequence. Apply the diagonalization technique to ±nd an explicit formula for the sequence. [4] (7) Find an orthogonal matrix Q that diagonalizes the symmetric matrix 1 1 3 1 3 1 3 1 1 . [4] Goes up to the end of § 6.4. 1...
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 Spring '10
 SOSPEDRAALFONSO
 Math, Linear Algebra, Algebra, Eigenvalues, Orthogonal matrix

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