Gauss Jordan Elimination & Reduced Row Echelon Form

This precalculus video tutorial provides a basic introduction into the gauss jordan elimination which is a process used to solve a system of linear equations by converting the system into an augmented matrix and using elementary row operations to convert the 3x3 matrix into its reduced row echelon form. You can easily determine the answers once you convert it to that form.

Introduction to Matrices:

Adding and Subtracting Matrices:

Scalar Multiplication of Matrices:

Solving Matrix Equations:

Multiplying Matrices:

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Gaussian Elimination & Row Echelon Form:

Gauss Jordan Elimination:

Gaussian Elimination With 4 Variables:

Inverse of a 2x2 Matrix:

Inverse of a 3x3 Matrix:

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Determinant of 2x2 and 3x3 Matrix:

Determinant of 4x4 Matrix:

Cramer's Rule - 2x2 Linear System:

Cramer's Rule - 3x3 Linear System:

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Final Exams and Video Playlists:

Full-Length Videos and Worksheets:

[MusantoSus]

This guy is a literal blessing; the only sad thing is that people come to him only when it's too late - the night before the final.

[mro]

It took me 5 days to fully understand Gauss-Jordan Elimination.

I have now, after many attempts, come to a conclusion that you ALWAYS have to do this when you start (the example is a 3x4 but the rule is for all):

- -
| 1 x x | x |
| x x x | x |
| x x x | x |
- -

- -
| 1 x x | x |
| 0 x x | x |
| x x x | x |
- -

- -
| 1 x x | x |
| 0 x x | x |
| 0 x x | x |
- -

After you have done these three steps you need to check if there’s a “1” in the middle of row two or three.

If there’s no “1” in the middle of row two but there’s a “1” in row three, you need to swap row two with row three.

If there’s no “1” in either, you have to find the pivot in row two and turn it into a “1”. These steps are the fundamental of Gauss-Jordan Elimination. The other steps will become clear after these steps.

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