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anonymous

  • 5 years ago

Matrix question

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  1. anonymous
    • 5 years ago
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  2. anonymous
    • 5 years ago
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    sorry dont do matrix graphing :P

  3. anonymous
    • 5 years ago
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    LOL

  4. anonymous
    • 5 years ago
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    R u there?

  5. anonymous
    • 5 years ago
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    HUH how did u get those equations?

  6. anonymous
    • 5 years ago
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    What question r u reading?

  7. anonymous
    • 5 years ago
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    I accidentally posted the wrong question but then I deleted it an reposted the right one

  8. anonymous
    • 5 years ago
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    recheck it it shldnt be abt traffic flow

  9. anonymous
    • 5 years ago
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    Ah, I clicked too fast before you did that, my bad. I'll look at your actual question now!

  10. anonymous
    • 5 years ago
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    Thanks lol

  11. anonymous
    • 5 years ago
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    Sorry abt that. i thought I deleted b4 u came

  12. anonymous
    • 5 years ago
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    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!

  13. anonymous
    • 5 years ago
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    I am in linear algebra but I am only in second chapter/second week

  14. anonymous
    • 5 years ago
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    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 \[\left(\begin{matrix} 0 & 1 \\ 0 & 0 \\ \end{matrix}\right)^2=0\]

  15. anonymous
    • 5 years ago
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    let me just solve that wait a sec

  16. anonymous
    • 5 years ago
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    oh ya i see

  17. anonymous
    • 5 years ago
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    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 \[\left(\begin{matrix} 0 & 1 & 0 \\ 0 & 0 & 1 \\ 0 & 0 & 0 \end{matrix}\right)^3=0\]

  18. anonymous
    • 5 years ago
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    In fact, any matrix that is strictly upper triangular (meaning that the main diagonal and everything below it is zero) is nilpotent!

  19. anonymous
    • 5 years ago
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    oh i see

  20. anonymous
    • 5 years ago
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    However, not all nilpotent matrices are of this form. Note that \[\left(\begin{matrix} 12 & -18 \\ 8 & -12 \\ \end{matrix}\right)^2=0\]

  21. anonymous
    • 5 years ago
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    Imperialist is on a roll :DDDD

  22. anonymous
    • 5 years ago
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    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.

  23. anonymous
    • 5 years ago
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    ok thanks for the explanation

  24. anonymous
    • 5 years ago
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    I will page u if I have another question

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