# How to solve for two variables in a 3x3 matrix?

#### xhellocoldworld

Hi. I have this question on my Pre-Calculus homework that honestly I have no idea what to do for. We never went over this specific type of problem in class (go figure) and I'm unable to find anything else helpful on the internet. The problem is to solve for the two variables in this 3x3 matrix:
I believe the determinant has already been given and it is 10. (The two previous problems are set up in this same way, simply with 2x2 matrices, and one of them said "hint: we know the determinant is 30" which is what the matrix was equal to.)
I am just not sure where to go from here. I wish I could offer some more beginning steps, but I'm totally stumped. I tried to begin to do the whole minor/cofactor thing by crossing out the first row and first column, but then the first element would be x, and I don't know if that's right/how it'd work.

I really will appreciate any help. (Happy)

#### skeeter

MHF Helper

$x(x+2) - 3(2x+8) - 1(2-4) = 10$

$x^2-4x-22 = 10$

$x^2-4x-32=0$

$(x-8)(x+4) = 0$

$x=8$ or $x=-4$

2 people

MHF Helper
Last edited:
2 people

#### topsquark

Forum Staff
This looks a bit complicated, but there is a specific example for a 3 x 3 determinate. The general version of this is called "expansion by minors."

-Dan

1 person

#### Plato

MHF Helper
Hi. I have this question on my Pre-Calculus homework that honestly I have no idea what to do for. We never went over this specific type of problem in class (go figure) and I'm unable to find anything else helpful on the internet. The problem is to solve for the two variables in this 3x3 matrix: View attachment 37304
I believe the determinant has already been given and it is 10. )
Look at this webpage.
If you do not know about wolframalpha.com then you should.
It is an invaluable resource on the WWW. You can spend time to explore what it can do for you.