1. ## Determinant

Assuming Det(AB) = Det(A) x Det(B) for 3x3 matrices prove that the determinant of

3 , a+b+c , a^3+b^3+c^3
a+b+c , a^2+b^2+c^2 , a^4+b^4+c^4
a^2+b^2+c^2 , a^3+b^3+c^3 , a^5+b^5+c^5

= (a+b+c)(b-a)^2(c-a)^2(a-b)^2

i was just going to work through the math but i dont really understand how the result given at the top will help me when working out the determinant as its is the cofactor times the 2x2 you get - the next cofactor times the 2x2 and so on.

2. Hi,
Originally Posted by rebirthflame
Assuming Det(AB) = Det(A) x Det(B) for 3x3 matrices prove that [...]

$\displaystyle \begin{vmatrix} 3 & a+b+c & a^3+b^3+c^3\\ a+b+c & a^2+b^2+c^2 & a^4+b^4+c^4\\ a^2+b^2+c^2 & a^3+b^3+c^3 & a^5+b^5+c^5\\ \end{vmatrix} = (a+b+c)(b-a)^2(c-a)^2(a-b)^2$
I suggest you try to find two matrices $\displaystyle A$ and $\displaystyle B$ such that
$\displaystyle AB=\begin{pmatrix} 3 & a+b+c & a^3+b^3+c^3\\ a+b+c & a^2+b^2+c^2 & a^4+b^4+c^4\\ a^2+b^2+c^2 & a^3+b^3+c^3 & a^5+b^5+c^5\\ \end{pmatrix}$