Question 976488
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If ALL the Determinants in a system of equations, then the equations are dependent and the system has infinite solutions.  Graphically, the equations all have identical ordered <i>n</i>-tuple solution sets, and therefore all represent the same line.


If the Determinant calculated from the coefficient matrix is zero but at least one of the other determinants is non-zero, then the system is <b><i>inconsistent</b></i> and the system has zero solutions.  Graphically, the equations represent either parallel, or possibly in the case of lines in *[tex \Large \mathbb{R}^n] space where *[tex \Large n\ >\ 2], skew lines. 


John
*[tex \LARGE e^{i\pi}\ +\ 1\ =\ 0]
My calculator said it, I believe it, that settles it

*[tex \Large \ \
*[tex \LARGE \ \ \ \ \ \ \ \ \ \