This preview shows pages 1–4. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: Solution for HW7 November 17, 2011 2.39 (a) AB = 7 14 39 28 ( AB ) C = 21 105 98 17 285 296 (b) BC = 5 15 20 8 60 59 A ( BC ) = 21 105 98 17 285 296 2.41 (a) A T = 1 3 2 4 (b) B T = 5 6 7 (c) ( AB ) T = 7 39 14 28 (d) A T B T = 5 15 10 40 2.51 (a) A 2 = 11 15 9 14 A 3 = 67 40 24 59 . (b) f ( A ) = 50 70 42 36 , g ( A ) = 1 2.60 (a) A n = 1 2 n 1 (b) B n = 1 n n ( n 1) 2 1 n 1 2.64 A = 1 2 1 3 1 2 2.68 (a) x = 4 , y = 1 , z = 3 . (b) x = 0 , y = 6 , z = any number. 2.69 Proof: (a) ( A + A T ) T = A T +( A T ) T = A T + A = A + A T . That is, A + A T is symmetric. (b) ( A A T ) T = A T ( A T ) T = A T A = ( A A T ) , which means that ( A A T ) is skewsymmetric. (c) Put B = A + A T 2 and C = A A T 2 . We can see that B is symmetric and C is skewsymmetric and A = B + C . 2.76 A = A H gives us 3 x + 2 i yi 3 2 i 1 + zi yi 1 xi 1 = 3 3 + 2 i yi x 2 i 1 + xi yi 1 zi 1 or x = 3 , y = 0 , z = 3 . 2 2.78 Proof (a) ( A + A H ) H = A H +( A H ) H = A H + A = A + A H , which shows that A + A H is Hermitian....
View
Full
Document
 Fall '08
 Feinberg,E

Click to edit the document details