Homework 8 - M341 H8 (S. Zhang) 1.1-2. 1. Use back...

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Unformatted text preview: M341 H8 (S. Zhang) 1.1-2. 1. Use back sbustitution to solve x 1 + 3 x 2 + 3 x 3 + x 4 = 5 3 x 2 + x 3- 3 x 4 = 1- x 3 + 3 x 4 =- 1 4 x 4 = 4 ans: (1.1:1c) From last equation, work upward. x 4 = 1 x 3 = 3 x 2 = 0 x 1 =- 2 2. Find the coefficient matrix x 1 + 3 x 2 + 3 x 3 + x 4 = 5 3 x 2 + x 3- 3 x 4 = 1- x 3 + 3 x 4 =- 1 4 x 4 = 4 ans: (1.1:2c) A = 1 3 3 1 3 1- 3- 1 3 4 3. Interpret each equation as a line and determine geometri- cally the number of solutions. x 1 + x 2 = 4 x 1- x 2 = 2 x 1 + 2 x 2 = 4- 2 x 1- 4 x 2 = 4 2 x 1- x 2 = 3- 4 x 1 + 2 x 2 =- 6 ans: (1.1:3) (a) Two crossing lines. Intersection (3 , 1). (b) Two parallel lines. No intersection/solution. (c) Two overlaping lines. All poinst C (1 ,- 1) are solu- tions. 4. Solve the system by row operations. x 1 +2 x 2- x 3 = 1 2 x 1- x 2 + x 3 = 3- x 1 + 2 x 2 3 x 3 = 7 ans: (1.1:6) 1 2- 1 | 1 2- 1 1 | 3- 1 2 3 | 7 - 2 r 1 + r 2 r 1 + r 3 1 2- 1 | 1- 5 3 |...
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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 8 - M341 H8 (S. Zhang) 1.1-2. 1. Use back...

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