anonymous
  • anonymous
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 upper-triangular m x n matrices
Mathematics
  • Stacey Warren - Expert brainly.com
Hey! We 've verified this expert answer for you, click below to unlock the details :)
SOLVED
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
schrodinger
  • schrodinger
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
anonymous
  • anonymous
Ah, I just don't get this stuff!
anonymous
  • anonymous
hehe wait a sec i am just checking :)
KingGeorge
  • KingGeorge
I'm pretty sure this is a vector space since it satisfies all the axioms need for a vector space.

Looking for something else?

Not the answer you are looking for? Search for more explanations.

More answers

anonymous
  • anonymous
it is a vector space that is forsure
anonymous
  • anonymous
you just have to go thru all the axioms which is a pain :)
anonymous
  • anonymous
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
anonymous
  • anonymous
umm if you show using real values it is easier
anonymous
  • anonymous
but i am not sure what ur prof wld want
anonymous
  • anonymous
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.
KingGeorge
  • KingGeorge
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.
anonymous
  • anonymous
well i doubt her prof wld accepy that :)
anonymous
  • anonymous
anyways if its closed under addition not neccesairy will it be cllosed under multiplication
KingGeorge
  • KingGeorge
Well, closure of addition implies that u+v is still a matrix, if u, v are upper-triangular matrices. Since addition is associative, and multiplying matrices by scalars is a property of matrices that is well-defined, all the axioms are satisfied. In a vector space, you never multiply vectors together.
anonymous
  • anonymous
kk but she still has to show that all the axioms are satisfied
KingGeorge
  • KingGeorge
Yes, but their proof are almost trivial once you've showed closure of addition.
anonymous
  • anonymous
True :)
anonymous
  • anonymous
umm brinethy u know how to show that all the 10 axioms r true?
anonymous
  • anonymous
I don't know how to do this with a general mxn matrix
anonymous
  • anonymous
showing that it's closed under scalar multiplication and vector addition, I mean.
anonymous
  • anonymous
give me a sec and i will do it
KingGeorge
  • KingGeorge
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.
anonymous
  • anonymous
Pippa, thank you very much for taking the time to do this for me. I can't tell you how much I appreciate it.
anonymous
  • anonymous
1 Attachment
anonymous
  • anonymous
well i just proved that they are closed under addition and scaler multiplication. Do u see how?
KingGeorge
  • KingGeorge
Aren't those all lower triangular matrices? not upper?
anonymous
  • anonymous
oh Sh* but it wld be the same thing
anonymous
  • anonymous
its a good thing u r around king
KingGeorge
  • KingGeorge
no problem at all.
anonymous
  • anonymous
umm there are still 8 more axioms that need to be proved
anonymous
  • anonymous
some of them take much longer to prive than others
anonymous
  • anonymous
These are the two main ones
anonymous
  • anonymous
R u still there?
anonymous
  • anonymous
Yeah, I stepped out. My dad had to tell me something
anonymous
  • anonymous
I'm opening your file right now
anonymous
  • anonymous
lol that is ok:)
anonymous
  • anonymous
So as long as it's closed under vector addition and scalar multiplication, the set is a vector space?
anonymous
  • anonymous
umm well u kind of have to prove the other axioms as well which is harder
anonymous
  • anonymous
and btw by accident i proved using lower traingles in stead of upper
anonymous
  • anonymous
Yes, I am aware of that
KingGeorge
  • KingGeorge
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)
anonymous
  • anonymous
y wld u need to do that?
anonymous
  • anonymous
I am just wondering cuz i dont remember ever doing that?
anonymous
  • anonymous
idk I just went thru every axiom
anonymous
  • anonymous
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
anonymous
  • anonymous
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
anonymous
  • anonymous
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
anonymous
  • anonymous
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
anonymous
  • anonymous
k gonna go study i hope i was a lil bit helpful :)
anonymous
  • anonymous
I will. And I really appreciate your help, thank you for taking the time to explain this stuff to me.
anonymous
  • anonymous
U r welcome its fun to teach others cuz that means I am comfortable enough in this area to explain it to others :) Gluck

Looking for something else?

Not the answer you are looking for? Search for more explanations.