mat67-2011-hw3

# mat67-2011-hw3 - coeﬃcient matrix(iii using the reduced...

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Homework Assignment #3 Math 67 UC Davis, Fall 2011 Homework due. Tuesday 10/18/11 at discussion section. Reading material. Read Sections 4.4–5.4 and 12.3.1–12.3.2 in the textbook. Problems 1. Solve the following problems in the textbook: (a) Calculational exercises 1, 2, 3 in Chapter 5. (b) Proof-writing exercise 4 in Chapter 5. 2. Solve each of the following homogeneous linear systems in 3 steps: (i) write the coeﬃcient matrix; (ii) use the Gaussian elimination technique to bring the system to Reduced Row-Echelon Form (RREF) by applying elementary row operations to the
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Unformatted text preview: coeﬃcient matrix; (iii) using the reduced row-echelon form, write the general form of a solution to the system. (a) ± x + 5 z = 0 y = 0 (b) x + 3 y + 0 z-w = 0-x-2 y-z + w = 0 y + w = 0 (c) ± x + 3 y = 0-x-2 y = 0 (d) ± x + 3 y = 0 3 x + 9 y = 0 (e) x + y + 5 z = 0 y-10 z = 0 2 z = 0 (f) ± x + y + 5 z = 0 2 x + 3 y-10 z = 0 (g) x 1 + 0 x 2-1 2 x 3-x 4 + x 5 = 0 2 x 1-x 2-3 x 3 + 3 x 4-x 5 = 0 x 1 + x 2 + 2 x 3 + x 4 + 3 x 5 = 0 x 1 + 0 x 2-1 2 x 3 + x 4 + x 5 = 0...
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