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Unformatted text preview: M341 H8 (S. Zhang) 1.12. 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.
 Fall '08
 Zhang
 Linear Algebra, Algebra, Equations

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