Algebra - Ch. 35: Systems of of Linear Eq. in 3 Variables (7 of 25) How to Evaluate a Determinant?

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We will learn how to evaluate the DETERMINANT of these system of linear equations in 3 variables:
Eqn. 1: x-y+4z=9
Eqn. 2: 5x+3y-6z=3
Eqn. 3: 3x+7y+4z=-1

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Fantastic. I feel tempted to put that into practice and write a mini equation-solving app just for fun. The only thing I didn't quite get is the sign matrix. To me it looks like you only used the top row for 1, 2 and 3. What is the application of the remaining ones in this particular problem? [flamingo?]

aram