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!