Mathematic Methods HW Solutions 16

Mathematic Methods HW Solutions 16 - Chapter 3 1 1 −2 0 ,...

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Unformatted text preview: Chapter 3 1 1 −2 0 , C= √ 1 1 52 1 1 −1 0 D= , C= √ 2 1 21 1 1 −1 0 D= , C= √ 1 1 21 1 21 0 , C= √ D= 2 5 −1 2 1 1i λ = 1, 3; U = √ 2i1 1 1 1−i λ = 1, 4; U = √ 1 3 −1 − i 1 2 −i λ = 2, −3; U = √ 5 −i 2 1 5 −3 − 4i λ = 3, −7; U = √ 5 5 2 3 − 4i √ −1 i√2 1 1 U = √1 −i 2 √ − 1 2 2 0 2 Reflection through the plane 3x − 2y − 3z = 0, no rotation √ 60◦ rotation about −i 2 + k and reflection through the √ plane z = x 2 180◦ rotation about i + j + k √ −120◦ (or 240◦ ) rotation about i 2 + j Rotation −90◦ about i − 2j + 2k, and reflection through the plane x − 2y + 2z = 0 45◦ rotation about j − k 1 f (1) + 4f (6) 2f (1) − 2f (6) f (M) = 5 2f (1) − 2f (6) 4f (1) + f (6) 1 1 + 4 · 64 2 − 2 · 64 1 1 + 4 · 610 2 − 2 · 610 M4 = M10 = 4 4 4+6 4 + 610 5 2−2·6 5 2 − 2 · 610 5 5 e 1 + 4e 2(1 − e ) eM = 4 + e5 5 2(1 − e5 ) 1 + 24 1 − 24 1 + 210 1 − 210 M4 = 23 M10 = 23 , 4 4 1−2 1+2 1 − 210 1 + 210 cosh 1 − sinh 1 eM = e3 − sinh 1 cosh 1 11.29 D = 11.30 11.31 11.32 11.41 11.42 11.43 11.44 11.47 11.51 11.52 11.53 11.54 11.55 11.56 11.58 11.59 12.2 12.4 12.6 12.14 12.15 12.16 12.17 12.18 12.19 12.21 12.22 12.23 16 2 11 0 4 0 5 0 7 0 2 2 3x − 2y = 24 12.3 10x = 35 2 2 2 2 2 12.5 x + 3y + 6z = 14 5x − 5y = 8 √ √2 2 2 2 2 2 3x + 3y − 3z = 12 12.7 3x + 5 y − z = 60 y = x with ω = k /m; y = −x with ω = 5k/m y = 2x with ω = 3k/m; x = −2y with ω = 8k/m y = 2x with ω = 2k/m; x = −2y with ω = 7k/m x = −2y with ω = 2k/m; 3x = 2y with ω = 2k/(3m) y = x with ω = 2k/m; x = −5y with ω = 16k/(5m) y = −x with ω = 3k/m; y = 2x with ω = 3k/(2m) y = 2x with ω = k /m; x = −2y with ω = 6k/m y = −x with ω = 2k/m; y = 3x with ω = 2k/(3m) y = −x with ω = k /m; y = 2x with ω = k /(4m) ...
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