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 3 years ago
Linear Algebra: Determine whether this is a vector space. Either show that the necessary properties are satisfied, or give an example that at least one of them is not.
The set of all uppertriangular m x n matrices
 3 years ago
Linear Algebra: Determine whether this is a vector space. Either show that the necessary properties are satisfied, or give an example that at least one of them is not. The set of all uppertriangular m x n matrices

This Question is Closed

brinethery
 3 years ago
Best ResponseYou've already chosen the best response.2Ah, I just don't get this stuff!

Pippa
 3 years ago
Best ResponseYou've already chosen the best response.3hehe wait a sec i am just checking :)

KingGeorge
 3 years ago
Best ResponseYou've already chosen the best response.0I'm pretty sure this is a vector space since it satisfies all the axioms need for a vector space.

Pippa
 3 years ago
Best ResponseYou've already chosen the best response.3it is a vector space that is forsure

Pippa
 3 years ago
Best ResponseYou've already chosen the best response.3you just have to go thru all the axioms which is a pain :)

Pippa
 3 years ago
Best ResponseYou've already chosen the best response.3umm i wonder if you can assign values to the matrix to show that all axioms are true or you just have to leave them as variables

Pippa
 3 years ago
Best ResponseYou've already chosen the best response.3umm if you show using real values it is easier

Pippa
 3 years ago
Best ResponseYou've already chosen the best response.3but i am not sure what ur prof wld want

brinethery
 3 years ago
Best ResponseYou've already chosen the best response.2It would probably have to be more formal mathematical language... he docked me when I was doing a proof with a 3x3 matrix one time.

KingGeorge
 3 years ago
Best ResponseYou've already chosen the best response.0All you would really need to show is that the set of upper triangular matrices is closed under addition which is obvious. The other axioms are properties of matrices, or follow directly from closure of addition.

Pippa
 3 years ago
Best ResponseYou've already chosen the best response.3well i doubt her prof wld accepy that :)

Pippa
 3 years ago
Best ResponseYou've already chosen the best response.3anyways if its closed under addition not neccesairy will it be cllosed under multiplication

KingGeorge
 3 years ago
Best ResponseYou've already chosen the best response.0Well, closure of addition implies that u+v is still a matrix, if u, v are uppertriangular matrices. Since addition is associative, and multiplying matrices by scalars is a property of matrices that is welldefined, all the axioms are satisfied. In a vector space, you never multiply vectors together.

Pippa
 3 years ago
Best ResponseYou've already chosen the best response.3kk but she still has to show that all the axioms are satisfied

KingGeorge
 3 years ago
Best ResponseYou've already chosen the best response.0Yes, but their proof are almost trivial once you've showed closure of addition.

Pippa
 3 years ago
Best ResponseYou've already chosen the best response.3umm brinethy u know how to show that all the 10 axioms r true?

brinethery
 3 years ago
Best ResponseYou've already chosen the best response.2I don't know how to do this with a general mxn matrix

brinethery
 3 years ago
Best ResponseYou've already chosen the best response.2showing that it's closed under scalar multiplication and vector addition, I mean.

Pippa
 3 years ago
Best ResponseYou've already chosen the best response.3give me a sec and i will do it

KingGeorge
 3 years ago
Best ResponseYou've already chosen the best response.0Scalar multiplication should already be given to you as a property of matrices. As for vector addition, choose two arbitrary m x n upper triangular matrices, and add them together. It should become pretty obvious that it's closed after that.

brinethery
 3 years ago
Best ResponseYou've already chosen the best response.2Pippa, thank you very much for taking the time to do this for me. I can't tell you how much I appreciate it.

Pippa
 3 years ago
Best ResponseYou've already chosen the best response.3well i just proved that they are closed under addition and scaler multiplication. Do u see how?

KingGeorge
 3 years ago
Best ResponseYou've already chosen the best response.0Aren't those all lower triangular matrices? not upper?

Pippa
 3 years ago
Best ResponseYou've already chosen the best response.3oh Sh* but it wld be the same thing

Pippa
 3 years ago
Best ResponseYou've already chosen the best response.3its a good thing u r around king

Pippa
 3 years ago
Best ResponseYou've already chosen the best response.3umm there are still 8 more axioms that need to be proved

Pippa
 3 years ago
Best ResponseYou've already chosen the best response.3some of them take much longer to prive than others

Pippa
 3 years ago
Best ResponseYou've already chosen the best response.3These are the two main ones

brinethery
 3 years ago
Best ResponseYou've already chosen the best response.2Yeah, I stepped out. My dad had to tell me something

brinethery
 3 years ago
Best ResponseYou've already chosen the best response.2I'm opening your file right now

brinethery
 3 years ago
Best ResponseYou've already chosen the best response.2So as long as it's closed under vector addition and scalar multiplication, the set is a vector space?

Pippa
 3 years ago
Best ResponseYou've already chosen the best response.3umm well u kind of have to prove the other axioms as well which is harder

Pippa
 3 years ago
Best ResponseYou've already chosen the best response.3and btw by accident i proved using lower traingles in stead of upper

brinethery
 3 years ago
Best ResponseYou've already chosen the best response.2Yes, I am aware of that

KingGeorge
 3 years ago
Best ResponseYou've already chosen the best response.0While you have to show a little more, the only other part that doesn't follow directly from those facts is that you need to find an inverse matrix (hint: multiply by 1 to get the inverse)

Pippa
 3 years ago
Best ResponseYou've already chosen the best response.3I am just wondering cuz i dont remember ever doing that?

Pippa
 3 years ago
Best ResponseYou've already chosen the best response.3idk I just went thru every axiom

brinethery
 3 years ago
Best ResponseYou've already chosen the best response.2Sorry guys, I am even more lost. I guess you have to go through all the axioms but I'm not getting a clear answer. I'll ask the instructor tomorrow, but he'll probably confuse me even more lol

Pippa
 3 years ago
Best ResponseYou've already chosen the best response.3LOL yes well you just went thru two axioms you just proved that it is closed under addition and that it is closed under scaler mutiplication

Pippa
 3 years ago
Best ResponseYou've already chosen the best response.3Like in ur textbook there shld be another 8 axioms that need to be proved liek one of them is u+v = v+u and (u+v)+w=u+(w+v) and many others

Pippa
 3 years ago
Best ResponseYou've already chosen the best response.3but it will take me hours to write them out unfortunately i dont have a tablet so like maybe ask ur prof to show u how

Pippa
 3 years ago
Best ResponseYou've already chosen the best response.3k gonna go study i hope i was a lil bit helpful :)

brinethery
 3 years ago
Best ResponseYou've already chosen the best response.2I will. And I really appreciate your help, thank you for taking the time to explain this stuff to me.

Pippa
 3 years ago
Best ResponseYou've already chosen the best response.3U r welcome its fun to teach others cuz that means I am comfortable enough in this area to explain it to others :) Gluck
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