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Tutorial 6 Solutions

# Tutorial 6 Solutions - -i 1 1 and D = 1 i 1-i 2 Let z = cos...

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Tutorial 6 Solutions MATH 1104 1-Last name: First name: 2-Last name: First name: 3-Last name: First name: 4-Last name: First name: 5-Last name: First name: ——————————————————————————- 1: Let A = 5 - 2 1 3 . (i): Find al eigenvalues of A and their corresponding eigenvectors for A . (ii): Diagonalize A . Solution: The characteristic equation is λ 2 - 8 λ +17 = 0 so λ 1 = 4 + i and λ 2 = λ 1 = 4 - i are the eigenvalues with the corresponding eigenvectors v 1 = 1 + i 1 and v 2 = v 1 = 1 - i 1 (ii) A = PDP - 1 where P = 1 + i 1
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Unformatted text preview: -i 1 1 and D = 1 + i 1-i . 2: Let z = cos( π/ 16) + i sin( π/ 16) and w = cos( π/ 8) + i sin( π/ 8). What is z 2 w ? (a) 1 √ 2 (1 + i ) (b) 1 √ 2 (1-i ) (c) 1 + i (d) 1-i (e) 1 3: What is the standard form of the complex number 3-4 i 1-2 i ? (a) 1-3 i (b) 2 5 + 11 5 i (c) 11 5 + 2 5 i (d) 2 5-11 5 i (e) 11 5-2 5 i 4: What is (1 + √ 3 i ) 3 ? (a) √ 3(1+ i ) (b) 1 √ 3 (1-i ) (c) 1-i (d) 1+ i (e)-8 1...
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