Gaussian Elimination & Row Echelon Form

This precalculus video tutorial provides a basic introduction into the gaussian elimination - a process that involves elementary row operations with 3x3 matrices which allows you to solve a system of linear equations with 3 variables. You need to convert the system of equations into an augmented matrix and use matrix row operations to write it in row echelon form. Next, you can convert back into a system of linear equations and solve using back substitution.

Full-Length Math & Science Videos:

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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:

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[taekwondotime]

This seems to be a common misunderstanding with matrices. *Echelon form is simply the final matrix after you've finished Gauss elimination* . (The matrix at 6:10.) It need only have 0's in the lower left-hand corner. *There is no requirement to have 1's along the main diagonal because they do not help in solving the problem* . They are simply wasted operations and are not done in practice. (Unless you want to do Gauss-Jordan elimination... which is also not used in practice.)

People seem to confuse the two. You only need 1's on the main diagonal if you're prepping for Gauss-Jordan elimination which then transforms the numbers in the upper right corner of the matrix to 0's as well. If you're not doing Gauss-Jordan, then don't worry about having 1's.

*Once you obtain the matrix @**6:10**, then we know that 4z = 8 and therefore z = 8/4 = 2* . From there we use back substitution to solve for the remaining variables.

FYI: This is straight out of my math textbook if you don't believe me.

*Source: Advanced Engineering Mathematics by Erwin Kreyszig*

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[ez]

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[paulvanbrakel]

For the people that get confused at 10:50: 'R3 = R1-R3 is the same as 'R3 = -R3 + R1. He writes it in a different way, but you're still working on 3R in both cases

[georgesadler]

MR. Organic Chemistry Tutor, this is an excellent introduction to the Gaussian Elimination Method and Row Echelon Form in classical Linear Algebra. Linear Algebra is very useful in different levels of mathematics.

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