Gaussian Elimination

Note:

These notes are imported from Notion. They’re not in the Atomic Notes style.

A matrix is in Row Echelon Form when it’s in it’s “nice form”. There’s 3 rules:

1. All $0$’s are at the bottom.
2. There is a leading $1$ in each row.
3. Each following leading $1$ is to the right of the one above it.

It is Reduced when each leading $1$ is the only one in it’s column.

It will look like a staircase.

ILA Math Notes has examples of bringing Matrices down to their (reduced) REF.

Just know the following:

The Reduced REF of Matrix A is directly influenced by the original Matrix A. Whereas if you just bring Matrix A to boring REF, the same original Matrix A could have multiple different REF.

The Rank is the number of leading 1’s.