Mathematic Methods HW Solutions 14

Mathematic Methods HW Solutions 14 - Chapter 3 14 10 0 0 0...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Chapter 3 14 10 0 0 0 , S = 0 0 −1 ; R is a 90◦ rotation about 01 0 1 a 90◦ rotation about the x axis. 0 −1 0 001 0 −1 ; From problem 30, RS = 1 0 0 , SR = 0 1 0 0 010 RS is a 120◦ rotation about i + j + k; SR is a 120◦ rotation about i − j + k. 180◦ rotation about i − k 120◦ rotation about i − j − k Reflection through the plane y + z = 0 Reflection through the (x, y ) plane, and 90◦ rotation about the z axis. 0 −1 0 7.30 R = 1 0 0 the z axis; S is 7.31 7.32 7.33 7.34 7.35 8.1 8.2 8.3 8.6 8.17 8.19 8.21 8.23 8.24 8.25 8.26 8.27 8.28 9.3 9.4 1 In terms of basis u = 1 (9, 0, 7), v = 9 (0, −9, 13), the vectors 9 are: u − 4v, 5u − 2v, 2u + v, 3u + 6v. 1 1 In terms of basis u = 3 (3, 0, 5), v = 3 (0, 3, −2), the vectors are: u − 2v, u + v, −2u + v, 3u. Basis i, j, k. 8.4 Basis i, j, k. 1 V = 3A − B 8.7 V = 3 (1, −4) + 2 (5, 2) 2 3 x = 0, y = 2 z 8.18 x = −3y , z = 2y x=y=z=w=0 8.20 x = −z , y = z x1 y1 z1 1 a 1 b 1 c1 x2 y2 z2 1 8.22 a2 b2 c2 = 0 x3 y3 z3 1 = 0 a 3 b 3 c3 x4 y4 z4 1 For λ = 3, x = 2y ; for λ = 8, y = −2x For λ = 7, x = 3y ; for λ = −3, y = −3x For λ = 2: x = 0, y = −3z ; for λ = −3: x = −5y , z = 3y ; for λ = 4: z = 3y , x = 2y r = (3, 1, 0) + (−1, 1, 1)z r = (0, 1, 2) + (1, 1, 0)x r = (3, 1, 0) + (2, 1, 1)z 1 2i 1 0 5i − 5 −10i 1 0 −5i 10 A† = 0 2 1 − i, A−1 = 10 −2i −1 − i −5i 0 0 2 00 2 0i3 1 i A† = −2i 2 0, A−1 = 0 3 6 −6 6i −2 −1 0 0 9.14 CT BAT , C−1 M−1 C, H √ 10.1 (a) d = 5 (b) d = 8 (c) d = 56 10.2 The dimension of the space = the number of basis vectors listed. One possible basis is given; other bases consist of the same number of independent linear combinations of the vectors given. (a) (1, −1, 0, 0), (−2, 0, 5, 1) (b) (1, 0, 0, 5, 0, 1), (0, 1, 0, 0, 6, 4), (0, 0, 1, 0, −3, 0) (c) (1, 0, 0, 0, −3), (0, 2, 0, 0, 1), (0, 0, 1, 0, −1), (0, 0, 0, 1, 4) . ...
View Full Document

This note was uploaded on 02/29/2012 for the course MHF 2312 taught by Professor Dr.chet during the Fall '11 term at UNF.

Ask a homework question - tutors are online