Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

What's the pattern here?

  1. Feb 24, 2009 #1
    1. The problem statement, all variables and given/known data

    Alright so apparently there is some pattern in finding these determinants:

    for the 2x2, the determinant of
    |1 1|
    |x y| is y - x

    for 3x3, the determinant of

    |1 1 1 |
    |x y z |
    |x^2, y^2, z^2| xy^2 - yx^2 - xz^2 +zx^2 + yz^2 - zy^2

    Apparently that can be factored (not sure how), and using the roots, there will be a pattern that you can observe for finding a determinant of a 4x4, 5x5, etc of the same form (1, x, x^2, x^3, etc.)

    How do you factor the 3x3 determinant, and what is the pattern?

  2. jcsd
  3. Feb 24, 2009 #2


    User Avatar
    Science Advisor
    Homework Helper

    Suppose you set x=y. What's the determinant of the matrix? What does this tell you about the factorization of the determinant polynomial? Now set x=z...
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook