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Calcmathlete

  • 3 years ago

Evaluate: \(\left[\begin{matrix}1 & 2 &1 & 3 \\2&3&2&0\\3&1&0&1\\0&0&3&2\end{matrix}\right]\)

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  1. Calcmathlete
    • 3 years ago
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    I got -102. Is it correct or did I get an arithmetic error somewhere?

  2. Zekarias
    • 3 years ago
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    I got -98

  3. Calcmathlete
    • 3 years ago
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    Hmm... Let me just double check everything here...

  4. Calcmathlete
    • 3 years ago
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    \[3\left[\begin{matrix}1 & 2 &3\\ 2 & 3 &0\\3&1&1\end{matrix}\right] - 2\left[\begin{matrix}1 & 2 &1\\ 2 & 3 &2\\3&1&0\end{matrix}\right]\]Did you end up doing this?

  5. TuringTest
    • 3 years ago
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    determinant?

  6. Calcmathlete
    • 3 years ago
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    I think so.

  7. TuringTest
    • 3 years ago
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    must be method of cofactors, eh?

  8. Calcmathlete
    • 3 years ago
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    Yup...

  9. asnaseer
    • 3 years ago
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    I get 72. But maybe I made a mistake. Might be worth looking at this to help: http://people.richland.edu/james/lecture/m116/matrices/determinant.html

  10. TuringTest
    • 3 years ago
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    I get 72 as well

  11. asnaseer
    • 3 years ago
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    Look down that web page at the section titled "Larger Order Determinants"

  12. TuringTest
    • 3 years ago
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    another source for ya http://tutorial.math.lamar.edu/Classes/LinAlg/MethodOfCofactors.aspx

  13. Calcmathlete
    • 3 years ago
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    Well, 72 is one of my answer choices... I did it again, but I got - 72? I think it's just an arithmetic error on my part. THanks guys!

  14. asnaseer
    • 3 years ago
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    yw :) - crosses fingers in the hope that he did make a mistake :)

  15. asnaseer
    • 3 years ago
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    *did NOT ...

  16. Calcmathlete
    • 3 years ago
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    Wait, one last thing, when I find the determinants of the 3 x 3, can I just use the diagonal method (I'm not sure of the name) or do I have to use minors?

  17. asnaseer
    • 3 years ago
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    as @TuringTest said, use the method of cofactors - see the links we gave you.

  18. Calcmathlete
    • 3 years ago
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    Ok, once again, thank you :)

  19. TuringTest
    • 3 years ago
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    the problem in what you did is that you forgot that all elements on the diagonals will give positive minors.

  20. TuringTest
    • 3 years ago
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    I phrased that poorly, not sure how to say it without giving away the answer

  21. asnaseer
    • 3 years ago
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    Also, determinants are usually written with straight lines on either side of the matrix elements - instead of the square brackets that you used.

  22. Calcmathlete
    • 3 years ago
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    Oh! I got it! And @asnaseer for some reason, I see them written both ways when doing school work?

  23. asnaseer
    • 3 years ago
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    Hmmm - ok, well I was taught that straight lines is what should be used. Maybe the notation differs from country to country?

  24. Calcmathlete
    • 3 years ago
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    Perhaps.

  25. TuringTest
    • 3 years ago
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    if it's left in brackets it should at least say \(\det\) in front of it In the US we use what @asnaseer said

  26. asnaseer
    • 3 years ago
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    Here is an example of how we are taught in the UK: http://www.intmath.com/matrices-determinants/matrix-determinant-intro.php

  27. asnaseer
    • 3 years ago
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    Also, when working with algebra, if you have a matrix A, then we would write its determinant as either:\[|A|\]or:\[det(A)\]

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