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# hw08 - equations(a-3-1 0 3-2-5 3 2-2 1-1 1 3 2 2-2 4 9 1 x...

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Math 110—Linear Algebra Fall 2009, Haiman Problem Set 8 Due Monday, Oct. 26 at the beginning of lecture. 1. For each of the following statements, either prove that it is true for all systems of m linear equations in n unknowns, or give a counterexample. (a) If the system has a unique solution, then m n . (b) If m n and the system is consistent, then the solution is unique. (c) Given a fixed coefficient matrix A , if the system Ax = b is consistent for every b , then m n . (d) If m n , then the system is consistent. 2. Use Gaussian elimination to find all solutions to each of the following systems of linear
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Unformatted text preview: equations: (a) -3-1 0 3-2-5 3 2-2 1-1 1 3 2 2-2 4 9 1 x 1 x 2 x 3 x 4 x 5 = 8 6-4 11 (b) -3-1 0 3-2-5 3 2-2 1-1 1 3 2 2-2 4 9 1 x 1 x 2 x 3 x 4 x 5 = -12-11-6-13 3. Section 3.4, Exercise 5...
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