# Thread: Finding Determinent of a Matrix

1. ## Finding Determinent of a Matrix

I have a matrix:

$\begin{bmatrix}x-4&4&0\\-1&x&0\\0&0&x-5 \end{bmatrix}$

I believe I've correctly used cofactor expansion to get:
(x-5)^(3+3) det( $\begin{bmatrix}x-4&4\\-1&x \end{bmatrix})$
I'm not sure what to do from this point, or if I'm doing it correctly at all... Help appreciated.
For instance, how would I find the cofactor of the new matrix?

2. Originally Posted by Hellreaver
I have a matrix:

$\begin{bmatrix}x-4&4&0\\-1&x&0\\0&0&x-5 \end{bmatrix}$

I believe I've correctly used cofactor expansion to get:
(x-5)^(3+3) det( $\begin{bmatrix}x-4&4\\-1&x \end{bmatrix})$
I'm not sure what to do from this point, or if I'm doing it correctly at all... Help appreciated.
For instance, how would I find the cofactor of the new matrix?
Why is (x-5) raised to the power of (3+3)?

"I'm not sure what to do from this point, ..." You should know how to get the determinant of a 2x2 matrix.

3. Originally Posted by mr fantastic
Why is (x-5) raised to the power of (3+3)?

"I'm not sure what to do from this point, ..." You should know how to get the determinant of a 2x2 matrix.
Sorry, I meant to raise (-1) to (3+3).
(x-4)(4)-(4)(-1)
4x-16+4
(x-5)(4x-12)

Do I equate that to zero or something?

4. $
\begin{bmatrix}x-4&4&0\\-1&x&0\\0&0&x-5 \end{bmatrix}
$

Could you do it like this:

$(x-4)(x)(x-5)+4(x-5)=x(x^2-9x+20)+4x-20=x^3-9x^2+24x-20$

?

You can try and factorise it if you like.