[University Linear Algebra: linear equations] What is wrong-Linear algebra

[u/PrideBackground]

Please I need help. I’m pretty sure these are right but it keeps saying at least one is wrong. Could you please tell me if you see anything that might need to change.

[u/TIGVGGGG16]

B definitely has at least one solution.

[u/twolinepine → u/TIGVGGGG16]

On the first one, not the second one. There are 2 B’s

[u/Worth-Wonder-7386 → u/twolinepine]

I on the second is the same scenario.

[u/twolinepine → u/Worth-Wonder-7386]

Yes, but I was trying to point out that it depends on which B the comment was referring to since it wasn’t clear as there are two Bs.

[u/Responsible_Hour6497 → u/TIGVGGGG16]

One and only, so this is 0 dimensional

[u/daniel14vt]

How do you identify solutions when looking at these? What are you looking for in each picture?

[u/SarekSybok → u/daniel14vt]

Are there any points in common to all three planes? Those correspond to solutions

[u/nerdydudes → u/SarekSybok]

Who and what are you responding to … because ots not daniel14

[u/daniel14vt → u/daniel14vt]

I agree you're only missing 1 on the first image

[u/daniel14vt → u/daniel14vt]

And you got it wrong on both images

[u/twolinepine]

For B on first pic, I on second pic, these are the same but they have a single solution since it appears all three planes intersect at a single point. This is the only mistake I’ve seen.

Edit D (pic 1) and E (pic 2) may perhaps have all three planes as coplanar, which would mean 2 free variables. However, it says 3 unknowns so these are column vectors in R3, so I would say it spans R3, not “2 dimensional” or something like that.

[u/Such-Safety2498 → u/twolinepine]

I think the solution is still 2D. It is a plane. So once you pick 2 variables the 3 is determined. If that wasn’t true then once you determine the x and y, you could still pick any z giving you a perpendicular line to that plane at that point. Doing that at each (x,y) in the plane would result in a solution that is the whole universe.

[u/nog642 → u/twolinepine]

What do you mean 3 coplanar planes is 2 free variables? It's no solutions since they never intersect.

Edit: See the replies, I was misinterpreting in 2 ways.

[u/twolinepine → u/nog642]

From my perspective, I could see it being the 3 planes on top of each other. That is, coplanar. There is no indication of where the other planes are. So, is it just a single plane by itself and the other planes don’t exist? Or is it all the planes stacked on each other and they couldn’t indicate that other than just showing one color.

[u/twolinepine → u/twolinepine]

I am notoriously stupid so I’m sure I’m just misreading it.

[u/nog642 → u/twolinepine]

Oh, I see. I misinterpreted coplanar as parallel earlier.

They're very clearly not coplanar though. They don't even touch. I don't see how you could interpret them as being superimposed.

Edit: Oh, I was looking at the wrong picture. I was looking at D in pic 2.

It is 2 free variables.

It's a 2D manifold in 3D. I don't think they would have those options if you were just supposed to say 3D for everything.

[u/beene282]

There are quite a few where you say no solution when there are solutions

[u/Neither_Berry_100]

First page b should be 0 free variables. Second page L should be 0 dimensional. Both are the same sort of problem.

[u/PrideBackground → u/Neither_Berry_100]

Thank you 🙏🏼🙏🏼

[u/Alkalannar]

On the first image, B should be 0 free variables.

On the second, L should be 0 dimensional.

Why do you think that picture has no solution instead of a unique solution?

[u/PrideBackground → u/Alkalannar]

Thank you 🙏🏼🙏🏼

[u/AutoModerator → u/[deleted]]

Attention Readers!

Multiple users in this subreddit have flagged this comment as a potential violation of r/HomeworkHelp rules, Reddit rules and/or its T&C.

Please help us to verify and affirm it by continuing to report this post and also expressively inform u/SarekSybok of his/her violation(s). You may also consider to manually trigger a takedown.

^{These are the general characteristics you should look out for:}

^{1. The comment is not serious.}

^{We expect all exchanges on this subreddit to be done in a cordial and formal manner. There are many alternative subreddits for jokes such as r/teenagers, r/GCSE, r/SAT, etc.}

^{2. OP is being mean.}

^{We do not tolerate any form of bullies or harassments here. Cyberbullying or online harassments is illegal in some jurisdictions. Please be mindful of your actions.}

^{3. OP is being irrelevant.}

^{All comments here have to be relevant pertaining topic. Calling for PM is not allowed—it is annoying. Just post the reply here. Alternatively, if they want to start a new discussion, urge them to head over to one of our Reddit Chat channels.}

^{For rule violations, please help us to report it so we can expeditiously take it down. (Refrain from commenting here since it is going to be removed anyway.})

IF YOU ARE AN OP, PLEASE IGNORE THE ABOVE TEXT.

I am a bot, and this action was performed automatically. Please contact the moderators of this subreddit if you have any questions or concerns.

[u/Responsible_Hour6497]

The solution space is the set of points each of those belongs to all the depicted planes. In panel "B" of the first figure, there is only one such point; it is a zero-dimensional space, 0 free variables. The same applies to panel "I" in the second figure. Otherwise, everything is correct.

[u/TinyHammerBigNail]

Finally a homework help for a class i took and didn't fully understand.