Assignment #5 - Stephanie Campbell due at 11:59pm EDT...

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Stephanie Campbell Assignment 5 MATH133, Fall 2009 due 10/13/2010 at 11:59pm EDT. You may attempt any problem an unlimited number of times. 1. (1 pt) Find the characteristic polynomial of the matrix A = 1 -3 0 0 2 3 -4 2 0 . p ( x ) = . 2. (1 pt) Find the eigenvalues of the matrix A = -27 -36 18 24 . The smaller eigenvalue is λ 1 = . The bigger eigenvalue is λ 2 = . 3. (1 pt) The matrix B = 6 6 5 0 5 6 0 0 -2 has threee distinct eigenvalues, λ 1 < λ 2 < λ 3 , where λ 1 = , λ 2 = , and λ 3 = . 4. (1 pt) The matrix C = 3 0 0 30 3 10 -13 -2 -6 has three distinct eigenvalues, λ 1 < λ 2 < λ 3 , where λ 1 = , λ 2 = , and λ 3 = . 5. (1 pt) The matrix C = 4 0 7 -7 -3 -7 0 0 -3 has two distinct eigenvalues, λ 1 < λ 2 : λ 1 = has multiplicity , and λ 2 = has multiplicity . 6. (2 pts) Let A = - 1 - 2 1 - 4 Compute the eigenvalues and eigenspaces of A : One eigenvalue of A is and the corresponding eigenspace is span { } The other eigenvalue of A is and its corresponding eigenspace is span { } 7. (2 pts) Let A = - 7 30 12 0 3 0 - 2 6 3 Show that -3, -1 and 3 are eigenvalues of A
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