Row Echelon Form (Matrix Conditions and Examples)

In order for a matrix to be in Row Echelon Form, it has to satisfy the two following conditions:

1. All rows that contain only zeroes must be at the bottom of the matrix.
2. The leftmost non-zero entry in any row (called the pivot) must be to the right of any pivot/non-zero leading entry in the rows above it.

0:00 Row Echelon Form conditions
0:17 Matrix example without zeroes in bottom row
0:39 Matrix example without cascading pivots
1:28 Matrix example that is in Row Echelon Form
1:51 Determining if examples are in Row Echelon Form
3:26 Scenarios where matrix is not in Row Echelon Form

#rowechelonform
#linearalgebra
#echelonform
#joecmath

[JoeCMath]

Informational Stops:
0:15 Two conditions for a matrix to be in row echelon form
0:34 Example where a row with all zeroes is not at the bottom of the matrix, failing to satisfy the first condition
1:15 Example where pivots do not satisfy the second condition (pivot stair-step pattern)
1:35 Example matrix that is in row echelon form


0:50 - 0:52 didn't know what to do with that highlight racing across the screen in the bottom row 🤣