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Homework 8

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

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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 0 3 1 - 3 0 0 - 1 3 0 0 0 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 | 1 4 2 | 8 (4 / 5) r 2 + r 3 1 2 - 1 | 1 - 5 3 | 1 22 / 5 | 44 / 5 Solution x = 1 1 2 5. Determine if it is in row echelon form, or reduced row echelon form.

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

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