# Factoring determinant

1. Jul 24, 2008

### takercena

1. The problem statement, all variables and given/known data
Code (Text):

| x       x^2   1  |
| x^2      x    1  |
| x^3    x^3   1  |

2. Relevant equations

none

3. The attempt at a solution
By factoring the matrix step by step.

Thanks :)

2. Jul 24, 2008

### Defennder

What's the problem here? Just use co-factor expansion along any row or column.

3. Jul 24, 2008

### jeffreydk

Take advantage of the fact that you have a column of ones in the third column...

$$\begin{vmatrix} x & x^2 & 1 \\ x^2 & x & 1 \\ x^3 & x^3 & 1 \end{vmatrix} = \begin{vmatrix} x^2 & x \\ x^3 & x^3 \end{vmatrix} - \begin{vmatrix} x & x^2 \\ x^3 & x^3 \end{vmatrix} + \begin{vmatrix} x & x^2 \\ x^2 & x \end{vmatrix}$$

So what does this end up being?

4. Jul 24, 2008

### takercena

Sorry for the question. I was confused by the question a moment ago because of language barrier.