C1_W2 - Row Echelon form in general - Wrong Row Echelon form

Course Q&A Math for Machine Learning Linear Algebra for Machine Learning and Data Sc...
1

Hello,

I am a bit confused about this one:

a + b + 2c = 12
3a - 3b -c = 3
2a - 1b - 6c = 24

The matrix
1 1 2
3 -3 -2
2 -1 6

In the lesson is said the row echelon form of the matrix is
1 1 2 = 12
0 -6 7 = -33
0 0 6 = 18 (getting 16.5 here)

From my calculation c is not 18 but 16.5 because the last row for me is
0 0 5.5

Am I doing something wrong?

Thanks
Carlo

2

Your -2 in the 2nd row of the matrix is incorrect. It should be -1.

3

As of April 4 2024 this still looks broken to me. In the w2 video "Row echelon form in general at 0:30 it shows this matrix:
1 1 2
3 -3 -1
2 -1 6
and claims the row echelon form is
1 1 2
0 -6 7
0 0 6

Before I share the problems I see in this computation, note this is a similar but different matrix than what Carlo_Tasca posted above. (it was probably revised since his post).

By my calculation the row echelon form is
1 1 2
0 -6 -7
0 0 5.5

So yes, the answer above is correct for the last row, but it’s wrong for the middle row as the example changed. Would be great to see this fixed, could be as simple as an inserted note so can keep the original video.

PS: Class is great!

Jeremy

4

Note that errors in the videos are not unusual. And they’re very difficult to update (especially when the course is taught by a guest instructor).

I’ll bring it up with the course staff. If there is an error, they can post a slide that warns about it.

5

Thanks for the quick response! Given these are hard to update, maybe publish an errata page such as for traditional text books? Maybe even post here and/or github? It’s not as clean as putting notes in the video but presumably much easier to maintain.

6

That’s what the course generally does, as a “reading page” that is inserted in the course sequence just ahead of the video.

Most courses don’t have a public repo.

7

Just to try and close out this thread:

  • It started in Jan 2021.
  • Since then, the video (and associated programming assignment) have been updated multiple times to both fix errors and make them more educational.
  • It is not possible (or at least not a good use of time) to research which posts in this thread were based on then errors in the materials, vs. typos in the thread itself. I suspect the augmented matrix in the OP of this thread contains at least two typos that were not in the 2021 version of the lecture. I’m not going to burn calories researching that any further.
  • The present version of the lecture “Row echelon form in general” shows this matrix, with an error as marked (in fuscia). I’ve submitted a support ticket to fix this error, or document it via an additional “reading” page.
    image
    image923×591 71.1 KB
  • The Gaussian Elimination programming assignment uses “row echelon form” to include having all of the pivots re-scaled to 1. That’s not strictly necessary, and makes comparisons with the lecture difficult.
  • Gaussian Elimination has precious little to do with machine learning. In the context of ML and AI education, Gaussian Elimination is akin to a mathematical parlor trick.