Elementary Row Operations - [Linear Algebra #1]

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