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Opening statement
So here I am, taking MA1101R Linear Algebra I - a required Math module for Computer Science undergraduate course at the National University Of Singapore. To make things slightly more interesting, I am going to try to make as many visualizations as I see fit, to demonstrate some of the concepts taught in lessons. This way, I guess I could say that Math is, in fact, useful to a web developer.
What's the use of Elementary Row Operations (ERO)?
- Two augmented matrices are row equivalent if one can be obtained from the other by a series of ERO.
- Two row equivalent augmented matrices have the same solution.
- By transforming an augmented matrix to its Row-Echelon Form or Reduced Row-Echelon Form through Gaussian Elimination and Gauss-Jordan Elimination respectively, we can find out its solution.
| Comparison | Observation in REF | Solution |
|---|---|---|
| More variables than equations | There is a non-pivot column in the REF, other than the last column | Infinitely many |
| Same number of variables and equations | Every column of REF is a pivot column, except the last | Only one |
| Inconsistent system | Has a row with nonzero last entry but zero elsewhere, or the last column is a pivot column | None |
A quick demo of elementary row operations
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