Linear Algebra 13a: Introduction to Elementary Matrices

[RelatedGiraffe]

Nice explanation. But the text at 14:08 is wrong because you already did that.

[RelatedGiraffe]

For the last matrix, wouldn't this be possible?

1. Add two of row one to row two
2. Subtract 2/3 of row two from row one
3. Multiply row one with -3

Or isn't it allowed to add/subtract a non-integer number times a row to/from another row, or multiply a row with a negative number? (I never heard you say anything about that) To me, it doesn't make any sense to forbid such operations in an elementary matrix. What is the reason for doing that?

[dannuttle]

I found this video very confusing at first until I realized that what is being discussed is in-place changes. One way (my way) to think about it is strictly in terms of the original two matrices, and the target. So for example, get 2 of the first column of the left matrix, and 3 of the third column, add them together, and put them in the first column of the target matrix. The approach here is making operations directly on one of the original two matrices (which will be used as the target matrix), and it was when I realized this that I saw why the order of the operations matters.

[Alekov_]

This felt like a more confusing sudoku :D

[tangolasher]

Please clarify: Before, you said the only 3 valid row operations are adding rows together, multiplying a row by a number, and switching rows, NOT COLUMNS. In this video, you say it's okay to switch columns to go from identity to an elementary matrix. Extremely confused, can you please explain? Thanks.

[elements-]

Can I switch between row and column operation while calculating elementary matrix?

[acruzp]

I wonder if anyone has a theory on orbits for these operations, i.e. which operations results in cyclic patterns in the matrix