Elementary Row Operations, Row Echelon Form, and Reduced Row Echelon Form

In this video we discuss how elementary row operations can be performed in a matrix to place it in row echelon form and reduced row echelon form. This is sometimes referred to as Gaussian Elimination and Gauss-Jordan Elimination, respectively. These are fundamental operations on matrices and is the foundation for more advanced linear algebra concepts that will be covered in future lectures.

Topics and timestamps:
0:00 – Introduction
6:53 – Row switching
8:12 – Row multiplication
9:33 – Row addition
16:15 – Row echelon form
35:52 – Reduced row echelon form
46:19 – Computing matrix inverse

#LinearAlgebra

[fionaryan]

AE501: A much needed refresher, thank you Professor Lum

[elijahleonen]

AE501: Great review of matrix reduction operations! Very helpful to understand these operations to see how our computational tools preform these calculations.

[lukewideman]

AE501 - originally skipped this, but had to refresh myself on REF and RREF! This video was an awesome explanation.

[BennettBoyd-hf]

AE501 - Great refresher on row operations

[HJ]

AE501: Glad I decided to watch this one before moving on. You break things down in a really easy-to-understand way! Also, I got an ad for a linear algebra tutor in the middle of this video lol

[solomondawit]

AE501: Great content and refresher. Thank you Professor Lum.

[suthakarmuthu]

Another great one from you professor!! Keeping the content of the E matrix is soemthing new learning for me!

[JonathanRiosRoman]

AE501 - I wished my undergrad professor were this clear with this topic! Excellent refresher.

[alviehaider]

AE 501 Never understood RREF and REF back in undergrad time. Video helped me clear it up better.

[AlejandroMartinez-nvri]

AE501: I initially skipped over this one as it was optional and quickly realized I needed to come back. It has been a while since I last saw linear algebra, really great refresher. The E matrix concept was another topic I dont fully remember, I ended up opening MatLab and testing some of the things you were saying to really convince myself. Thank you, great video!

[MarcoIacoviello-rw]

AE 501: thanks for putting these videos together

[tonykuenzli]

AE501 - This brings back a lot of "fond" memories doing reduced row echelon form and matrix inverses by hand in undegrad!

[BenLandes]

Good refresher! It's all coming back

[BrianaStaheli-gfjg]

AE501: Great review, especially with how these reduction operations relate to the inverse of the matrix. Never really understood that previously.

[tranpham]

AE501. I learned a lot of experience from this video. I appreciate for your helpful video.

[maxschreiber]

AE501: Like others, I originally skipped this but came back when I realized I was in too deep. Great review!

[Chuan-YuTsai]

AE501: Now I know why do we need to put the matrix in upper triangular form.
In 33:46, matrix E4, the bottom-right element of the matrix should be -6.

[Richard_Le]

AE501 Is there a method or rule which makes performing row reduction more manageable when complex numbers are involved?