Mathematic Methods HW Solutions 18

Mathematic Methods HW Solutions 18 - Chapter 3 18 10 −1 i...

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Unformatted text preview: Chapter 3 18 10 −1 i 15.7 AT = A= 1 0 −1 −i A−1 = 1 −i 0 −i BT AT = (AB)T −2 −6 3i 5i 2 2 1 BT AC = 1 − 3i −1 − 5i −1 AB = 2 0 0 2 0 −i C− 1 A = BT C = − 3 1 1 −1 −5 −1 AT BT , BAT , ABC, ABT C, B−1 C, and CBT are meaningless. 1 −i 1 −3i 0 6i 1 0 A−1 = 1 −i −2 15.8 A† = 0 −3 3i −2i 0 −i 3 0 −3 d 1 1 1 + (n−1)d −(n−1) R1 − R2 + (n−1)2 1 nR2 nR1 R , 15.9 A = = −A12 (n−1)d d f 1− A† = 1 0 −1 −i n 15.10 M = 1− d f2 nR1 − f1 1 − 1 f2 + d f1 d 1− −→ − − → 15.13 Area = 1 P Q × P R = 7/2 2 d f1 f2 , 1 = f f1 +f2 −d f1 f2 , det M = 1 15.14 x = −x, y = −y , 180◦ rotation 15.15 x = −y , y = x, 90◦ rotation of vectors or −90◦ rotation of axes 15.16 x = y , y = −x , z = z , 90◦ rotation of (x, y ) axes about the z axis, or −90◦ rotation of vectors about the z axis 15.17 x = x, y = −y , z = −z , rotation of π about the x axis 15.18 1 (1, 1) 15.19 6 (1, 1) 15.20 1 (1, 1) −2 (0, 1) 1 (1, −4) 9 (1, −1) 15.21 0 (1, −2) 15.22 1 (1, 0, 1) 15.23 1 (1, 1, −2) 5 (2, 1) 4 (0, 1, 0) 3 (1, −1, 0) 5 (1, 0, −1) 4 (1, 1, 1) 15.24 2 (0, 4, 3) 7 (5, −3, 4) −3 (5, 3, −4) √ 1 1√ 0 20 −1 15.25 C = √ ,C= 1 2 −1 1 2√ √ √ √ 142 1/√2 1/ √ 17 √ √2 15.26 C = , C− 1 = 17 − 17 1/ 2 −4/ 17 5 √ 15.27 3x 2 − y 2 − 5z 2 = 15, d = 5 2 2 2 15.28 9x + 4y − z = 36, d = 2 2 2 2 15.29 3x + 6y − 4z = 54, d = 3 2 2 2 15.30 7x + 20y − 6z = 20, d = 1 15.31 ω = (k/m)1/2 , (7k/m)1/2 15.32 ω = 2(k/m)1/2 , (3k/m)1/2 ...
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