For the first part, I understand how the determinant is a polynomial
in the form of t^n.
The first part of the determinant that would be calculated would be
the diagonal, (a11)(a22)(a33)..(ann). That would give me the equation
The resulting equation would end in
t^n +- .... +- a11a22a33..ann. My first question is, is there an
easier way to prove this, or is this good enough.
For part b, I'm not sure if I was supposed to come up with a different
coefficient, besides 1. I did some examples with n = 3,4,5 and I
always got that the coefficient was 1.
For part c I got that the constant from part a (+- a11a22..ann) would
be added to the opposite diagonal (+-a1n a2n-1...an1).
I'm not sure if I did that right! Thanks so much for your help!
Nov 20th 2008, 12:14 PM
By proving this by induction on when you expand along on of the cofactors.