anonymous
  • anonymous
Matrix question
Mathematics
katieb
  • katieb
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
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anonymous
  • anonymous
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anonymous
  • anonymous
sorry dont do matrix graphing :P
anonymous
  • anonymous
LOL

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anonymous
  • anonymous
R u there?
anonymous
  • anonymous
HUH how did u get those equations?
anonymous
  • anonymous
What question r u reading?
anonymous
  • anonymous
I accidentally posted the wrong question but then I deleted it an reposted the right one
anonymous
  • anonymous
recheck it it shldnt be abt traffic flow
anonymous
  • anonymous
Ah, I clicked too fast before you did that, my bad. I'll look at your actual question now!
anonymous
  • anonymous
Thanks lol
anonymous
  • anonymous
Sorry abt that. i thought I deleted b4 u came
anonymous
  • anonymous
Ah yes, a very cool problem! Let me think of what answer to give you. What class are you in actually, since that might decide how much depth I should go into!
anonymous
  • anonymous
I am in linear algebra but I am only in second chapter/second week
anonymous
  • anonymous
Okay, I'll just spit out a bunch of things and we'll go from there. First off, 2x2 cases are boring, so I'll probably go a bit higher for some things I say! Note that \[\left(\begin{matrix} 0 & 1 \\ 0 & 0 \\ \end{matrix}\right)^2=0\]
anonymous
  • anonymous
let me just solve that wait a sec
anonymous
  • anonymous
oh ya i see
anonymous
  • anonymous
But note that you also have that \[\left(\begin{matrix} 0 & 0 & 1 \\ 0 & 0 & 0 \\ 0 & 0 & 0 \end{matrix}\right)^2=0\] and you have that \[\left(\begin{matrix} 0 & 1 & 0 \\ 0 & 0 & 1 \\ 0 & 0 & 0 \end{matrix}\right)^3=0\]
anonymous
  • anonymous
In fact, any matrix that is strictly upper triangular (meaning that the main diagonal and everything below it is zero) is nilpotent!
anonymous
  • anonymous
oh i see
anonymous
  • anonymous
However, not all nilpotent matrices are of this form. Note that \[\left(\begin{matrix} 12 & -18 \\ 8 & -12 \\ \end{matrix}\right)^2=0\]
anonymous
  • anonymous
Imperialist is on a roll :DDDD
anonymous
  • anonymous
I'm sure you will learn a lot more about this matrices later in your class, I will tell you two things you should notice about all of them. 1. All of them have determinant = 0 2. If A is the nilpotent matrix and k is the earliest integer such that A^k=0, then the trace of A, A^2, A^3, ..., A^(k-1)=0. Since trace(A^m) for m greater than or equal to k is obviously zero (since all of those matrices are zero), then trace(A^m)=0 for all m>0.
anonymous
  • anonymous
ok thanks for the explanation
anonymous
  • anonymous
I will page u if I have another question

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