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# tutorial9 - Section 5.4 4 • Let z 1 = 3-2 i and z 2 =-2 i...

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Tutorial #9 - MAT 1332A - Fall 2009 November 16, 2009 Let A = 4 0 - 2 2 5 4 0 0 5 . Find the eigenvalues and eigenvectors of A . Answer : λ 1 = 5 is an eigenvalue whose corresponding eigenvectors are v 1 = - 2 0 1 and v 2 = 0 1 0 . The other eigenvalue is λ 2 = 4 with corresponding eigenvector v 3 = - 1 2 0 . Section 5.1: 20 Section 5.2: 2, 16 (in addition, verify whether or not the equilibrium is stable based on Definition 5.2; and then confirm your answer by using the Stability Theorem (Theorem 5.1)) Section 5.4: 4
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Unformatted text preview: Section 5.4: 4 • Let z 1 = 3-2 i and z 2 =-2 + i . Write: (a) z 1 + 2 z 2 and z-1 2 as a + bi where a and b are real numbers (b) z 1 in polar coordinates, that is, as re iθ or ( r cos θ,r sin θ ) • Let A = 1-2-3 1 4 2-3 4 . Find: (a) the determinant of A . Then, conclude that A is invertible. (b) A-1 by row reducing [ A | I ] to [ I | A-1 ]. Answer : A-1 = 8 3 1 10 4 1 7 / 2 3 / 2 1 / 2 1...
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