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anonymous

  • one year ago

Evaluate the determinant of the matrix [8. 3 -2] [-1 3 2] [ 5 -1 1]

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  1. DanJS
    • one year ago
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    scalar triple product

  2. anonymous
    • one year ago
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    what?

  3. UsukiDoll
    • one year ago
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    cofactor expansion... that's needed to shrink the matrix down to a 2 x 2

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

  5. anonymous
    • one year ago
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    How?

  6. DanJS
    • one year ago
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    do you know a 2 by 2 determinant?

  7. anonymous
    • one year ago
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    yes! i just don't know how to find the determinant for a 3x3 matrix

  8. DanJS
    • one year ago
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    Determinant of 2 by 2 matrix = a*d - cd [a b] [c d]

  9. DanJS
    • one year ago
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    ok...

  10. UsukiDoll
    • one year ago
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    ad - bc for determinant of a 2 x 2 matrix for a 3 x 3 matrix we have to use cofactor expansion.

  11. anonymous
    • one year ago
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    how do i do cofactor expansion?

  12. DanJS
    • one year ago
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    |dw:1438052983671:dw|

  13. UsukiDoll
    • one year ago
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    Cofactor expansion expanding a row ... find the minors and the cofactors of the first row entries ( you can choose second row or third row entries but the sign pattern is different).

  14. DanJS
    • one year ago
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    |dw:1438053078307:dw|

  15. DanJS
    • one year ago
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    Cover first column, 8*det of that 2x2 is the first of 3 terms

  16. DanJS
    • one year ago
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    look up determinant of 3 x 3 matrix.. lol this is alot of drawing

  17. UsukiDoll
    • one year ago
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    the signs for the 3 x 3 matrix is like a checkerboard |dw:1438053171537:dw| that's why I use the first drawing a lot.

  18. UsukiDoll
    • one year ago
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    * first row signs

  19. DanJS
    • one year ago
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    yeah i just remember the second is minus

  20. UsukiDoll
    • one year ago
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    |dw:1438053270643:dw|

  21. UsukiDoll
    • one year ago
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    cut row one cut column one cut row one cut column two cut row one cut column three

  22. UsukiDoll
    • one year ago
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    |dw:1438053376916:dw|

  23. UsukiDoll
    • one year ago
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    ok I'm going to clean this up a bit.. but where I circled the row and column... you draw a line to cross them out... you should be left with 4 numbers... that's your 2 x 2 matrix. now you can take the determinant of those matrices...

  24. UsukiDoll
    • one year ago
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    |dw:1438053458361:dw|

  25. UsukiDoll
    • one year ago
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    |dw:1438053534643:dw|

  26. UsukiDoll
    • one year ago
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    |dw:1438053599579:dw| normally we would have a + sign but that negative -2 on the first row third column entry changes that.

  27. UsukiDoll
    • one year ago
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    |dw:1438053728550:dw| so we should have this equation after we have done cofactor expansion. Now we can take the determinant of the 2 x 2 matrix and combine like terms. The final answer for the determinant of the 3 x 3 matrix should be just a single number

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