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liliy

  • 2 years ago

what is diagnolization in linear algebra?

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  1. TuringTest
    • 2 years ago
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    I'm kind of weak in this area, so I'm just going to shoot you a link http://tutorial.math.lamar.edu/Classes/LinAlg/Diagonalization.aspx I'm sure somebody can explain it in their own words though... @UnkleRhaukus @nbouscal

  2. liliy
    • 2 years ago
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    thanks

  3. TuringTest
    • 2 years ago
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    @Callisto @Chlorophyll how are you guys with linear algebra? wanna help?

  4. liliy
    • 2 years ago
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    im totally lost. fml. my final is tomoro!!

  5. eliassaab
    • 2 years ago
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    Why don't you ask a specific question? Your question is too general and it takes time to answer all aspects of it.

  6. liliy
    • 2 years ago
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    okay: use the diagonlization theomr to find eignevalues of A and baisis for each eignespace: A= [ 2 -1 -1 1 4 1 -1 -1 2] =[ 1 -1 0 [ 3 0 0 [ 0 -1 -1 -1 1 -1 0 2 0 -1 -1 -1 0 -1 1] 0 0 3] -1 -1 0]

  7. liliy
    • 2 years ago
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    i dont even understand what to do here!

  8. eliassaab
    • 2 years ago
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    First find \[Det( A - \lambda I) \]

  9. liliy
    • 2 years ago
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    of what? A?

  10. eliassaab
    • 2 years ago
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    A is your matrix.

  11. liliy
    • 2 years ago
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    bec the 3 matrix udner it is: PD(P-1)

  12. eliassaab
    • 2 years ago
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    \[ Det(A-\lambda I)=-\lambda ^3+8 \lambda ^2-21 \lambda +18=(\lambda -3)^2 (2-\lambda ) \] So it has 3 as a double eigenvalue and 2.

  13. liliy
    • 2 years ago
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    \[-\lambda^3+8\lambda^2-20\lambda+18\]

  14. eliassaab
    • 2 years ago
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    -21 instead of -20

  15. liliy
    • 2 years ago
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    dang it. how? isnt it 4 lambda 8 and 8 ?

  16. eliassaab
    • 2 years ago
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    Now we have to find the eigenspace of 2 and the eigenspace of 3

  17. liliy
    • 2 years ago
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    okay so how do we do it?

  18. liliy
    • 2 years ago
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    A-3? A-2I?

  19. eliassaab
    • 2 years ago
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    Find X such that AX = 2 X and Y such AY =3Y Y1={-1, 0, 1} Y2={-1, 1, 0} X={1, -1, 1} Y1, and Y2 is a basis for the eigenspace of 3 X is a basis for the eigensapce 2

  20. liliy
    • 2 years ago
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    wooahhh. hold on. how did u do that? where are those y1 vextor from??

  21. eliassaab
    • 2 years ago
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    I have to go to sleep now. Try to unersatnd how I got what I got. Bye.

  22. liliy
    • 2 years ago
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    thnaks

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