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gaussian_elimination_remarks
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| gaussian_elimination_remarks [2015/02/04 18:17] – rupert | gaussian_elimination_remarks [2016/02/11 11:18] (current) – rupert | ||
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| - | ===== Observations about Gaussian elimination ===== | ||
| - | |||
| We know that we can apply [[EROs]] to any augmented matrix into [[REF]]. | We know that we can apply [[EROs]] to any augmented matrix into [[REF]]. | ||
| Line 36: | Line 34: | ||
| * So in this situation we //always// have infinitely many solutions. | * So in this situation we //always// have infinitely many solutions. | ||
| + | /* | ||
| === Observation 3: homogeneous systems === | === Observation 3: homogeneous systems === | ||
| Line 50: | Line 49: | ||
| * This system is necessarily consistent, since $(0, | * This system is necessarily consistent, since $(0, | ||
| * If $n<m$, then by the previous observation there are infinitely many solutions. | * If $n<m$, then by the previous observation there are infinitely many solutions. | ||
| + | */ | ||
gaussian_elimination_remarks.1423073832.txt.gz · Last modified: by rupert