# Thread: Matrix equation involving determinants

1. ## Matrix equation involving determinants

The question:

Consider the equation

$\displaystyle det$\left( \begin{array}{ccc} x - 1 & y - 2 & z + 1 \\ 1 & 0 & 2 \\ 2 & -1 & 0 \end{array} \right)$$ = 0

Show that the equation represents the Cartesian equation of a plane.

My attempt:
I'm not really sure how to interpret this. The equation is that the determinate = 0. How does a determinate represent the equation of a plane? Or are they referring to the first row of the matrix?

Any assistance would be great!

2. If you compute that determinant, you'll obtain a expression of the form $\displaystyle Ax+By+Cz+D$ . Then, $\displaystyle Ax+By+Cz+D=0$ is the equation of a plane (if $\displaystyle (A,B,C)\neq (0,0,0)$) .

Regards.

Fernando Revilla

3. Ahh, that was easy! Thanks.