Mathematic Methods HW Solutions 13

Mathematic Methods HW Solutions 13 - Chapter 3 13 6.8 5x2...

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Unformatted text preview: Chapter 3 13 6.8 5x2 + 3y 2 = 30 6.9 AB = 0 0 0 0 6.10 AC = A D = BA = 11 12 33 36 5/3 −3 −1 2 4 5 1 6.15 − −2 −2 2 2 3 22 1 6.17 A−1 = 4 4 6 8 2 3 B−1 AB = −2 −2 1 1 6.19 A−1 = −3 7 1 −4 6.20 A−1 = 5 7 −1 1 6.21 A−1 = −2 5 3 4 1 −7 6.22 A−1 = 12 1 6.13 22 44 −11 −22 1 3 1 0 −2 6 −2 11 1 6 −3 5 6.16 8 4 22 1 1 −1 0 1 B−1 = −2 0 −1 1 2 1 B−1 A−1 B = −4 6 2 6.14 8 −2 4 −1 −5 −4 1 2 2 −2 −2 −2 −4 −2 −1 0 −1 4 2 , (x, y ) = (5, 0) −1 3 , (x, y ) = (4, −3) −2 2 2 −1 4 , (x, y, z ) = (−2, 1, 5) −1 −1 40 −1 3 , (x, y, z ) = (1, −1, 2) −5 3 cos k 0 0 sin k , cos k A = I cos k = 6.30 sin k A = A sin k = 0 cos k sin k 0 cosh k sinh k cos k i sin k ek A = , eikA = sinh k cosh k i sin k cos k cos θ − sin θ 6.32 eiθB = sin θ cos θ In the following, L = linear, N = not linear. 7.1 N 7.2 L 7.3 N 7.4 L 7.5 L 7.6 N 7.7 L 7.8 N 7.9 N 7.10 N 7.11 N 7.12 L 7.13 (a) L (b) L 7.14 N 7.15 L 7.16 N 7.17 N ◦ 7.22 D = 1, rotation θ = −45 7.23 D = 1, rotation θ = 210◦ √ 7.24 D = −1, reﬂection line x + y = 0 7.25 D = −1, reﬂection line y = x 2 7.26 D = −1, reﬂection line x = 2y 7.27 D = 1, rotation θ = 135◦ −1 0 0 1 0 0 0 cos θ − sin θ 7.28 0 cos θ − sin θ , 0 sin θ cos θ 0 sin θ cos θ 0 01 7.29 0 −1 0 −1 00 , ...
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