Homework 9 - M341 H9 (S. Zhang) 1.3-4. 1. Find 2 A- 3 B , (...

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Unformatted text preview: M341 H9 (S. Zhang) 1.3-4. 1. Find 2 A- 3 B , ( aA ) T- (3 B ) T , AB , BA . A = 3 1 4- 2 1 1 2 2 B = 1 2- 3 1 1 2- 4 1 • ans: (1.3:1(c-f),) 2 A- 3 B = 3 2 2 5- 3- 1- 4 16 1 ( aA ) T- (3 B ) T = 3 5- 4 2- 3 16 2- 1 1 AB = 8- 15 11- 4- 3- 1- 6 6 BA = 5 5 8- 10- 1- 9 15 4 6 2. Find AB 3 5 1- 2 2 2 1 1 3 4 1 4- 2 6- 4 8- 6 ( 1 2 3 ) • ans: (1.3:2(a,b),) 3 5 1- 2 2 2 1 1 3 4 1 = 15 19 4 4- 2 6- 4 8- 6 ( 1 2 3 ) = not defined 3. Write the system as a matrix equation. 3 x 1 + 2 x 2 = 1 2 x 1- 3 x 2 = 5 x 1 + x 2 = 5 2 x 1 + x 2- x 3 = 6 3 x 1- 2 x 2 + x 3 = 7 2 x 1 + x 2 + x 3 = 4 x 1- x 2 + 2 x 3 = 2 3 x 1- 2 x 2- x 3 = 0 • ans: (1.3:4) Ax = b , where A, x, b are 3 2 2- 3 , x 1 x 2 , 1 5 Ax = b , where A, x, b are 1 1 2 1- 1 3- 2 2 , x 1 x 2 x 3 , 5 6 7 Ax = b , where A, x, b are 271 1 1- 1 2 3- 2- 1 , x 1 x 2 x 3 , 4 2 4. Find A 2 , A 3 , A 2 n , A 2 n +1 A = 1 / 2- 1 / 2- 1 / 2- 1 / 2- 1 / 2 1 / 2- 1 / 2- 1 / 2- 1 / 2- 1 / 2 1 / 2- 1 / 2- 1 / 2- 1 / 2- 1 / 2 1 / 2 • ans: (1.3:11) A 2 = I A 3 = A A 2 n = I A 2 n +1 = A 5. Show A n = 0 for n ≥ 4, A = 1 1 1 •...
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This homework help was uploaded on 04/07/2008 for the course MATH 341 taught by Professor Zhang during the Fall '08 term at University of Delaware.

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Homework 9 - M341 H9 (S. Zhang) 1.3-4. 1. Find 2 A- 3 B , (...

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