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Determinant of a 3X3 matrix

  1. Feb 16, 2008 #1
    M= |3-2x^3_____-4+2x^2+4x^3______0|

    find the determinant.

    * I put the underscores for spacing.

    3. The attempt at a solution

    I first tried finding det(A) as if it was a regular matrix of numbers, but that doesn't seem to work. So I'm really not sure how to find the determinant for a matrix of polynomial equations. Where would you actually start?
  2. jcsd
  3. Feb 16, 2008 #2


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    Well, one can use the fact that the third column has two zeros as entries.

    Think about

    + - +
    - + -
    + - +
  4. Feb 16, 2008 #3
    I'm not quite getting what I'm supposed to see from the 2 zeros. The way I worked it out before was using the normal determinant method of a11(a22*a33-a32*a23)-a12...etc. Would that not be the correct way to find a determinant for this type of matrix?
  5. Feb 16, 2008 #4


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    It should work! If it does not work, check your calculation. It's really the same as the determinant of a matrix of numbers. The fact that there are two zeroes will make the final result not too awful looking. But it's the usual formula for the determinant of a 3 by 3 matrix.

    EDIT: give your answer (before expanded out) and we can check if you made a mistake
    Last edited: Feb 16, 2008
  6. Feb 16, 2008 #5


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    That would be one way. The co-factor expansion (or determinant expansion by minors) can be done on any column or row! If one does is using the third column, one sees a33|A33|, where A33 is the 3,3 minor.


    See the examples here - http://en.wikipedia.org/wiki/Laplace_expansion - using first row or second column. One can also use the third row or third column.
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