Set 5 Solutions (1).pdf - ESE 318-02 Fall 2018 Homework...

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ESE 318-02, Fall 2018 Homework Set #5 (14 problems) Due Tuesday, Oct. 2 1. Zill 8.6.3 and 8.6.6. 2. Zill 8.6.8. 3. Zill 8.6.20, but use Zill Theorem 8.6.2 (i.e., cofactors/adjoint method). 4. Find the inverse of the matrix A below, when a , b and c are all non-zero. c b a A 0 0 0 0 0 0 5. Prove that if A is symmetric and invertible, then so is its inverse. That is, if A T = A , then ( A -1 ) T = A -1 . (Hint: T T T B C BC for any compatible matrices B and C .) 6. Find the eigenvalues and eigenvectors of the matrix A below. 5 1 5 1 A 7. Zill 8.8.10. Also determine if the given matrix is diagonalizable, and if so, determine P and D . 8. Zill 8.8.17. Also determine if the given matrix is diagonalizable, and if so, determine P and D . 9. Zill 8.8.21. Also determine if the given matrix is diagonalizable, and if so, determine P and D . 10. Without doing any real work, find the eigenvalues and eigenvectors of A below. 7 0 0 0 11 0 0 0 3 A 11. Consider the matrix Abelow.A=
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12. Consider the matrix Abelow. 13. Zill 10.1.4 14. Zill 10.1.11
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ESE 318-02, Fall 2018 Solutions 1. Zill 8.6.3 and 8.6.6. Both non-singular. 9 5 9 4 9 1 9 1 1 5 4 1 1 9 1 9 4 5 det 1 4 1 5 A A A 3 2 3 1 3 1 3 1 2 1 2 2 2 2 3 1 3 2 det 2 A A A 2. Zill 8.6.8 Singular. 0 42 42 0 42 56 77 2 det 7 4 1 14 11 0 0 3 2 A A 3. Zill 8.6.20, but use Zill Theorem 8.6.2 (i.e., cofactors/adjoint method) 9 2 9 1 9 4 9 1 9 5 9 2 9 2 9 1 9 5 1 2 1 4 1
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