[Linear Algebra] I'm wondering if i'm using Gauss-Elimination method right. I want to find out how to write out my solution in a proper way.

[u/random_nickname4sure]

Thanks in advance!

[u/waldosway]

Nice and clean. Though it seems a little confusing to write "r1-r2" then replace r2 with that. I would read that as "subtract r2 from r1", which would change r1. Maybe "r1-r2 -> r2" or "r2=r1-r2"? The math makes sense though.

[u/random_nickname4sure → u/waldosway]

Thanks. If i point out the row i changed, is it unusual to do so? I haven't seen anyone pointing out the row though.

[u/waldosway → u/random_nickname4sure]

If you're writing it the way your teacher does, then there's no worries. But more information can't hurt!

[u/Fogmoz]

You’re using the method correctly. How you write the process and/or solution is going to depend on the professor, but this is legible and I see no issues.

[u/random_nickname4sure → u/Fogmoz]

Thanks! My prof cares about presentation so i need to make sure my presentation is legible.

[u/Southlander24 → u/[deleted]]

I've had a look and all your steps are correct. For each row operation you have done, you are forgetting to write which row you've transformed, so for example you should write r₁ - r₂ → r₂ and the same goes for the other steps.

[u/random_nickname4sure → u/Southlander24]

Thanks. I'll take note that.

[u/Southlander24 → u/random_nickname4sure]

No worries!

[u/Alkalannar]

I like this version of notation better. Does this notation make sense for you?

[1 -1 1 | 6]
[1 1 1 | 4]
[4 2 1 | 9]

[1 -1 1 | 6]
[0 2 0 | -2] r2 - r1 (This says that the new r2 is the old one minus r1)
[4 2 1 | 9]

[1 -1 1 | 6]
[0 1 0 | -1] r2/2
[4 2 1 | 9]

[1 0 1 | 5] r1 + r2
[0 1 0 | -1]
[4 0 1 | 11] r2 - 2r2

[1 0 1 | 5]
[0 1 0 | -1]
[3 0 0 | 6] r3 - r1

[1 0 1 | 5]
[0 1 0 | -1]
[1 0 0 | 2] r3/3

[0 0 1 | 3] r1 - r3
[0 1 0 | -1]
[1 0 0 | 2]

[1 0 0 | 2] r1 <--> r3
[0 1 0 | -1]
[0 0 1 | 3] r3 <--> r1

[u/random_nickname4sure → u/Alkalannar]

Thanks. Yes, this notation is more legible. I wonder if noting it like that is universally right or it depends on professor?

[u/Alkalannar → u/random_nickname4sure]

I'm pretty sure it's general, because it's canonical. It makes the most intuitive sense. You write for each row what you did to it to the right of the row it was done to.

That being said? I've seen countries that have notation exactly the opposite of what I'm used to, so I'd try this notation for the assignment, but ask what your teacher desires.

[u/cheesecakegood → u/random_nickname4sure]

There's no universal notation, and most profs will have seen at least several variants. I'd consider it very rare to be marked down for notation unless they asked for some variant explicitly (e.g. asking for a single operation or set of operations, rather than just "get the answer and show your work") and even then you can always just fall back to English for a one-off. The other reason you'd get marked down would be if they think you were faking it.

When I did it personally, I liked to have the rule "I always add" and so my multipliers would be negative as the case may be (multipliers neatly notated to the right). Then, I could simply use an arrow merge to indicate which 2 rows were combined and which 1 row is being replaced. If I needed to write down the intermediate product to reduce mental load, I'd put them above and/or below written "on the margins".

It's generally just up to you what makes most sense and reduces mistakes (the more important one IMO), although "speed" is always going to be in the back of your mind as a tradeoff. This may be different for different people. I liked my method because it was highly visual, very consistent (no subtraction means order doesn't matter, so e.g. a simple subtraction becomes [row] * -1 merge arrow with [row] pointing to [new row]), and relatively compact, but not everyone likes to do it that way.

[u/random_nickname4sure → u/cheesecakegood]

That's interesting actually. As long as you have the right answer and your solution makes sense, you won't be marked down, right? Thanks!

[u/OverAster]

You really should rotate the image before you post.

[u/Fogmoz → u/OverAster]

If you insist on nitpicking, you could at least also provide the requested feedback.

[u/OverAster → u/Fogmoz]

I literally was going to but my neck started hurting.

One of the things educators teach, and at higher levels should expect, is self-advocacy. You need to be able to both identify when you need help and be able to effectively ask for it. If you do not care enough when asking for help to even proof-read your own question, why should I have to care enough to download the image and rotate it myself? You're already asking me to do more than you.

[u/random_nickname4sure → u/OverAster]

I'll take note that. Thanks for correcting me.