- #1
astonmartin
- 23
- 0
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| is 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? Does the determinant vanish at some point?