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anonymous
 4 years ago
Matrix question
anonymous
 4 years ago
Matrix question

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anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0sorry dont do matrix graphing :P

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0HUH how did u get those equations?

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0What question r u reading?

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0I accidentally posted the wrong question but then I deleted it an reposted the right one

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0recheck it it shldnt be abt traffic flow

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0Ah, I clicked too fast before you did that, my bad. I'll look at your actual question now!

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0Sorry abt that. i thought I deleted b4 u came

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0Ah 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
 4 years ago
Best ResponseYou've already chosen the best response.0I am in linear algebra but I am only in second chapter/second week

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0Okay, 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
 4 years ago
Best ResponseYou've already chosen the best response.0let me just solve that wait a sec

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0But 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
 4 years ago
Best ResponseYou've already chosen the best response.0In fact, any matrix that is strictly upper triangular (meaning that the main diagonal and everything below it is zero) is nilpotent!

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0However, not all nilpotent matrices are of this form. Note that \[\left(\begin{matrix} 12 & 18 \\ 8 & 12 \\ \end{matrix}\right)^2=0\]

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0Imperialist is on a roll :DDDD

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0I'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^(k1)=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
 4 years ago
Best ResponseYou've already chosen the best response.0ok thanks for the explanation

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0I will page u if I have another question
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