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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
 2 years ago
 2 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
 2 years ago
 2 years ago

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

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

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

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

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

PippaBest ResponseYou've already chosen the best response.3
umm 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
 2 years ago

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

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

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

KingGeorgeBest ResponseYou've already chosen the best response.0
All 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.
 2 years ago

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

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

KingGeorgeBest ResponseYou've already chosen the best response.0
Well, 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.
 2 years ago

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

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

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

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

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

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

KingGeorgeBest ResponseYou've already chosen the best response.0
Scalar 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.
 2 years ago

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

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

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

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

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

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

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

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

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

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

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

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

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

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

KingGeorgeBest ResponseYou've already chosen the best response.0
While 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)
 2 years ago

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

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

brinetheryBest ResponseYou've already chosen the best response.2
Sorry 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
 2 years ago

PippaBest ResponseYou've already chosen the best response.3
LOL 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
 2 years ago

PippaBest ResponseYou've already chosen the best response.3
Like 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
 2 years ago

PippaBest ResponseYou've already chosen the best response.3
but 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
 2 years ago

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

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

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