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anonymous

  • one year ago

ind the value of -6 -3 -5 5 7 -6 3 9 9

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  1. jim_thompson5910
    • one year ago
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    determinant of this matrix?

  2. anonymous
    • one year ago
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    -6

  3. jim_thompson5910
    • one year ago
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    can you post a screenshot of the full thing?

  4. anonymous
    • one year ago
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    I can't im sorry

  5. jim_thompson5910
    • one year ago
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    I'm confused what the full question is exactly

  6. anonymous
    • one year ago
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    finding the value

  7. anonymous
    • one year ago
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    it's only missing the brackets

  8. jim_thompson5910
    • one year ago
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    ok so this? \[\Large \left|\begin{array}{ccc} -6 & -3 & -5\\ 5 & 7 & -6\\ 3 & 9 & 9\\ \end{array}\right|\]

  9. anonymous
    • one year ago
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    yes

  10. jim_thompson5910
    • one year ago
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    ok so this is a determinant

  11. jim_thompson5910
    • one year ago
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    have you learned that term?

  12. anonymous
    • one year ago
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    I don't think i have

  13. jim_thompson5910
    • one year ago
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    |dw:1443314924015:dw|

  14. jim_thompson5910
    • one year ago
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    ok here is one method to do a determinant of a 3x3 matrix

  15. jim_thompson5910
    • one year ago
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    step 1) focus on the first two columns (circled) |dw:1443315068425:dw|

  16. jim_thompson5910
    • one year ago
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    copy those columns to the right of the matrix bar |dw:1443315093066:dw| keep the order the same

  17. jim_thompson5910
    • one year ago
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    we now have this extended matrix |dw:1443315131877:dw|

  18. jim_thompson5910
    • one year ago
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    step 2) draw diagonals that start at the top and face south east. I circled the terms eg: -6, 7 and 9 are the first group of terms |dw:1443315174379:dw|

  19. jim_thompson5910
    • one year ago
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    now multiply out the terms in each subgroup -6*7*9 = -378 -3*(-6)*3 = 54 -5*5*9 = -225

  20. jim_thompson5910
    • one year ago
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    then add up the products -378+54+(-225) = -549

  21. jim_thompson5910
    • one year ago
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    step 3) repeat the last step, but now we're going in the northeast direction |dw:1443315369919:dw|

  22. jim_thompson5910
    • one year ago
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    multiply out the subgroups 3*7*(-5) = -105 9*(-6)*(-6) = 324 9*5*(-3) = -135 add up the products -105+324+(-135) = 84

  23. jim_thompson5910
    • one year ago
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    the sum from step 2 was -549 the sum from step 3 was 84 subtract the sums like so -549-84 = -633 and that wraps up the problem

  24. jim_thompson5910
    • one year ago
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    It's a long process, but over time it should come easier with more practice

  25. anonymous
    • one year ago
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    thank you so much, it really seems a bit complicated but im starting to understand :3 @jim_thompson5910

  26. jim_thompson5910
    • one year ago
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    this page has a similar example http://www.sparknotes.com/math/algebra2/systemsofthreeequations/section3.rhtml

  27. DanJS
    • one year ago
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    Isn't that the same thing as doing the scalar triple product

  28. DanJS
    • one year ago
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    volume of parallellpipedd

  29. DanJS
    • one year ago
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    spaned by the three vectors

  30. DanJS
    • one year ago
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    (A x B) * C

  31. jim_thompson5910
    • one year ago
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    yes I think a 3x3 matrix determinant is involved somewhere in that

  32. DanJS
    • one year ago
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    vector cross product scalar triple product determinant |dw:1443320363438:dw|

  33. DanJS
    • one year ago
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    same thing, i just always remembered that way

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