6.2_bzca5e - Section 6.2 Inconsistent and Dependent Systems...

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Section 6.2 Inconsistent and Dependent Systems and Their Applications
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Gaussian Elimination to Systems Without Unique Solutions
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Possible Positions for Three Planes Inconsistent Systems Dependent Systems
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Possible Positions for Three Planes Linear systems can have one solution, no solution, or infinitely many solutions. We can use Gaussian elimination on systems with three or more variables to determine how many solutions such systems have. In the case of systems with no solution or infinitely many solutions, it is impossible to rewrite the augmented matrix in the desired form with 1s down the main diagonal from upper left to lower right, and 0s below the 1s. The system has no solution if one of the rows in the row-echelon form is a false statement, ie. 0x+0y+0z=5. The system has infinitely many solutions if the three planes intersect in more than one point. This is when all but one variable can be written in terms of the one variable.
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The Matices for Infinitely Many Solutions and No Solution
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This document was uploaded on 10/26/2011 for the course FKP bmfp at UTEM Chile.

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6.2_bzca5e - Section 6.2 Inconsistent and Dependent Systems...

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