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anonymous

  • one year ago

Find the value

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  1. anonymous
    • one year ago
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  2. anonymous
    • one year ago
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    @jim_thompson5910 how do i do this?

  3. jim_thompson5910
    • one year ago
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    |dw:1443914556285:dw|

  4. jim_thompson5910
    • one year ago
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    the vertical bars mean "determinant"

  5. anonymous
    • one year ago
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    So how would I find the value?

  6. jim_thompson5910
    • one year ago
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    step 1) copy the first 2 columns and write them to the right of the vertical bar |dw:1443914670674:dw|

  7. anonymous
    • one year ago
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    Ok and then what?

  8. jim_thompson5910
    • one year ago
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    step 2) group up the elements into subgroups by circling the elements along the diagonals like this (see circled) |dw:1443914609410:dw|

  9. jim_thompson5910
    • one year ago
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    step 3) multiply out the numbers in the sub groups |dw:1443914648908:dw|

  10. jim_thompson5910
    • one year ago
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    step 4) add up those products 6+0+(-3)=3 We'll use this number later. Let's call this "sum A"

  11. jim_thompson5910
    • one year ago
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    step 5) this is very similar to step 2, but now we're circling these diagonals (see below) |dw:1443914771771:dw|

  12. jim_thompson5910
    • one year ago
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    step 6) multiply out the numbers in the sub groups |dw:1443914811735:dw|

  13. jim_thompson5910
    • one year ago
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    step 7) add up those products 0+1+(-18)=-17 We'll use this number later. Let's call this "sum2"

  14. jim_thompson5910
    • one year ago
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    sorry sum B, but I guess it doesn't matter as long as you're consistent

  15. jim_thompson5910
    • one year ago
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    step 8 (final step) subtract the two sums sum A - sum B = 3 - (-17) = 3 + 17 = 20 so the determinant of this matrix is 20

  16. anonymous
    • one year ago
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    Value = determinant right? Same thing?

  17. jim_thompson5910
    • one year ago
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    hmm I messed up somewhere, let me think

  18. jim_thompson5910
    • one year ago
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    oh nvm, I just typed it into the calc wrong

  19. anonymous
    • one year ago
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    Ok so the final answer (value) is 20?

  20. jim_thompson5910
    • one year ago
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    \[\Large \left|\begin{array}{ccc}1&2&-1\\3&-2&1\\0&1&-3\end{array}\right| = 20\] i.e., the determinant of this matrix is 20

  21. anonymous
    • one year ago
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    thx

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