jerri-1-7 - Section 1.7 "Special Systems" of...

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Section 1.7 "Special Systems" of Equations SOME THEOREMS I. Given a system of linear equations, exactly one of the following possibilities holds: (A) The system has infinitely many solutions. (B) The system has no solution. (C)The system has exactly one solution. What happens if we have more unknowns than equations? Let’s look at a couple of examples.
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10 2 4 01 2 1 Here, 13 23 24 21 xx += −= so 42 12 x x x x =− − =+ 33 x x = There are infinitely many solutions. Second example: 11 2 0 000 1 From the second line, we see this has no solution. If we have 3 unknowns and 2 equations, is there a way to get a unique solution? An Example with a unique solution: 1001 0102 0013    1 2 3 1 2 3 x x x = = =
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Recall: With a unique solution, each variable equals a number. II. If a system of linear equations has fewer equations than unknowns then it cannot have a unique solution. Examples What can you say about the solution set for the described system: 1. The system has 3 equations and 4 unknowns.
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This note was uploaded on 11/11/2008 for the course MATH 1114 taught by Professor Jhengland during the Fall '08 term at Virginia Tech.

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jerri-1-7 - Section 1.7 "Special Systems" of...

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