# Finding values that make a determinate = 0

1. Oct 16, 2009

### DanielJackins

1. The problem statement, all variables and given/known data

Given the matrix A = {a, 3, 8}{a, -3, 4}{7, -4, a} find all values of a that make det(A) = 0.

(each {} is a row in the matrix, 3x3)

3. The attempt at a solution

I've expanded it out using the Cofactor theorem, ie. a11c11 + a21c21 + a31c31, and I come out with a polynomial, -2(3a^2+8a-126) which I equate to 0. Solving for the quadratic gives ugly roots which I can't see being correct.

Thanks for any help

2. Oct 16, 2009

### whs

Doing a very quick calculation, are you sure your '-126' shouldn't be '126'? (When you factor out the -2, shouldn't you have a positive 126 left?)

3. Oct 16, 2009

### nicksauce

Well according to maple your determinant is correct. You should really trust the math instead of your intuition about what you can see being correct.

4. Oct 16, 2009

### DanielJackins

Huh, it was correct :P I just figured the answer would be integers. Thanks for the help :)