Mathematic Methods HW Solutions 12

Mathematic Methods HW Solutions 12 - Chapter 3 5.33 5.35...

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Unformatted text preview: Chapter 3 5.33 5.35 5.37 5.39 5.40 5.41 5.43 5.45 6.1 6.2 6.3 6.4 6.5 12 5.34 11/10 √ 43/15 5 5.36 3 Intersect at (1, −3, 4) 5.38 arc cos 21/22 = 12.3◦ √ t1 = 1, t2 = −2, intersect at (3, 2, 0), cos θ = 5/ 60, θ = 49.8◦ √ ◦ t1 = √ = −1, t2 = 1, intersect at (4, −1, 1), cos θ√ 5/ 39, θ = 36.8 14 5.42 1/√5 √ 20/ √ 21 5.44 2/ 10 d = 2, t = −1 −5 10 1 24 5 −1 A−B= 1 1 15 5 5A = 10 25 AB = −2 11 11 A2 = 16 −6 3B = 3 BA = 8 21 8 27 6 12 A+B = B2 = 13 39 64 2 18 det(5A) = 52 det A −2 −2 −6 17 1 −1 BA = A+B= 1 2 −2 6 −1 5 3 −9 9 −25 14 A−B= A2 = B2 = −1 1 −5 14 04 10 −25 −3 12 5A = 3B = −5 15 06 7 −1 0 4 −1 2 212 1 −1 3 1 AB = 3 BA = 6 A + B = 3 1 1 3 9 5 0 16 341 13 1 1 10 4 0 −1 2 2 B2 = 3 3 A2 = 0 1 6 A − B = 3 −3 −1 3 1 −1 15 0 1 −3 6 1 3 30 5 0 10 6 3 det(5A) = 53 det A 3B = 0 5A = 15 −5 0 9 −3 0 0 25 5 12 10 2 12 5 1 7 5 12 BA = 0 2 1 −9 C2 = 6 4 8 3 −17 −3 −1 −2 7 4 20 14 4 1 20 C3 = 20 CB = 1 19 −8 −2 −9 1 −5 32 12 36 46 14 −36 7 91 C2 B = 53 CBA = 40 22 1 −13 −9 −8 −2 1 −29 8 8 2 2 8 10 3 −7 30 −13 T T AA = A A= 2 3 1 −4 −13 30 2 −7 −4 41 20 −2 2 14 4 2 4 BBT = −2 BT B = 4 18 2 4 10 21 −2 −3 14 1 1 2 5 CT C= −2 CCT = 1 21 −6 −3 5 14 1 −6 2 AB = ...
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