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Math Help - Matrix equation involving determinants

  1. #1
    Senior Member
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    Matrix equation involving determinants

    The question:

    Consider the equation

    det\[\left( \begin{array}{ccc}<br />
x - 1 & y - 2 & z + 1 \\<br />
1 & 0 & 2 \\<br />
2 & -1 & 0 \end{array} \right)\] = 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!
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  2. #2
    MHF Contributor FernandoRevilla's Avatar
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    If you compute that determinant, you'll obtain a expression of the form Ax+By+Cz+D . Then, Ax+By+Cz+D=0 is the equation of a plane (if (A,B,C)\neq (0,0,0)) .

    Regards.

    Fernando Revilla
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  3. #3
    Senior Member
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    Ahh, that was easy! Thanks.
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