What's the pattern here?

  • #1

Homework Statement



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?

Thanks!
 

Answers and Replies

  • #2
Dick
Science Advisor
Homework Helper
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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...
 

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