# What's the pattern here?

#### astonmartin

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| 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?

#### Dick

Homework Helper
Start with the 3x3 case. The pattern is that the determinant vanishes in the cases x=y, x=z and y=x. Do you see why? Each of those tells you a factor of the determinant.

### The Physics Forums Way

We Value Quality
• Topics based on mainstream science
• Proper English grammar and spelling
We Value Civility
• Positive and compassionate attitudes
• Patience while debating
We Value Productivity
• Disciplined to remain on-topic
• Recognition of own weaknesses
• Solo and co-op problem solving