**Unformatted text preview: **[1] (4) Let A = 1-3 3 3-5 3 6-6 4 . Find the eigenvalues of A and a basis for each of the associated eigenspaces. [4] (5) Diagonalize the following matrix. -2-1 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 k-1 + a k-2 ) / 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
- SOSPEDRA-ALFONSO
- Math, Linear Algebra, Algebra, Eigenvalues, Orthogonal matrix