Linear Algebra 2

Linear Algebra 2 - , we have 2 0 3 b | 4 0 1 b | 1 0 0 8-8...

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Problem 2. Consider the following system 2 x - 3 y = 1 y + bz = 1 4 x + 2 y + 8 z = a For which values of a and b does this system have (a) no solution ? (b) infinitely many solutions ? (c) a unique solution ? Solution. Applying the elementary row operations - 2 R 1 + R 3 , 3 R 2 + R 1 and - 8 R 2 + R 3 to the augmented matrix 2 - 3 0 | 1 0 1 b | 1 4 2 8 | a
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Unformatted text preview: , we have 2 0 3 b | 4 0 1 b | 1 0 0 8-8 b | a-10 , and so this system has (a) no solution if a 6 = 10 and b = 1 . (b) infinitely many solutions if a = 10 and b = 1 . (c) a unique solution if a ∈ R and b 6 = 1 2...
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This note was uploaded on 05/12/2010 for the course MATH 2602 taught by Professor Costello during the Spring '09 term at Georgia Tech.

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