HW8 - -----= 2 1 6 1 2 3 2 2 A . Also find the defect...

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ME 391: FALL 2007 HW 8 (Due Date: Nov. 7, 2007) 1. (a). Given = 5 3 1 0 2 0 4 13 2 A , (i). Evaluate ) det( A by the cofactor expansion method i.e by expanding along any row or column. (ii). If A is invertible, determine 1 - A by finding ) ( A adj . 2. (a). Given 7 3 2 1 3 2 1 3 2 1 = c c c b b b a a a , evaluate the determinants of the following matrices, without expanding by cofactors (use properties of determinants): (i). A = 3 3 3 2 2 2 1 1 1 a b c a b c a b c , (ii). - - - = 3 2 2 1 3 2 2 1 3 2 2 1 2 3 3 3 6 2 c c c c b b b b a a a a B (b). Find the values of k for which - = k k k 2 3 3 5 0 1 C is singular. 3. Solve the following system of equations by (a). Finding the inverse of the coefficient matrix by elementary row operations. (b). Cramer’s rule 1 = + - z y x 2 2 2 = + + z y x 3 2 3 - = - + z y x 4. (a). Find the eigenvalues and corresponding eigenvectors of
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Unformatted text preview: -----= 2 1 6 1 2 3 2 2 A . Also find the defect corresponding to each eigenvalue. (b). For what values of will ---= 1 5 5 1 5 B have the eigenvalues 0,-4,4? Find the eigenvectors corresponding to these eigenvalues. 5. Practice Problems (do not submit for grading) Exercises 8.4: Problems 2, 4, 14, 16, 18, 28 Exercises 8.5: Problems 4, 6, 8, 13, 14, 24, 34, 37, 39 Exercises 8.6: Problems 2, 14, 24, 26, 31, 34, 38, 40, 44, 49, 54 Exercises 8.7: Problems 1, 7, 11, 12, 13 Exercises 8.8: Problems 2, 4, 6, 11, 13, 17, 21, 23, 25...
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