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Unformatted text preview: + 5) . Under what condition is A is diagonalizable? Problem 5. Condisder L ( y ) = y + 2 y + 2 y . (a) Solve L ( y ) = 0. (b) Solve L ( y ) = cos( x ). Problem 6. Consider the following matrix A = 24 5 1 21 4 3 1 5 . (a) What is the determinant of A ? (b) What is the trace of A ? (c) What are the eigenvalues of A ? Problem 7. Consider the matrix A = 1 0 1 0 0 2 0 1 1 . Find the eigenvalues and eigenvectors of A . Is A diagonalizable? Justify your answer. . Problem 8. Let A and B be two invertible matrices. Show that AB and BA have the same characteristic polynomial....
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 Spring '07
 Trangenstein
 Math

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