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Cramer's rule


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Because if you have an infinite number of solutions, the determinant of the coefficient matrix (the denominator) will be zero.

And as you know, division by zero doesn't work.

 

If you want, I'll show an example as soon as I figure out how to write matrices in latex.

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I think I understand what you meant by "infinite solutions" now, so here goes an example:

Equation system:

equation 1: 1*x + 1*y = 0

equation 2: 1*x + 1*y = 0

Of course, the system of equations is solved for any x=-y, meaning there is an infinite number of solutions (x=-y=1, x=-y=2, ...).

Applying Cramer's rule, you get [math] x = \frac{\text{det} \left[ \begin{matrix} 0 & 1 \\ 0 & 1 \end{matrix} \right]}{\text{det} \left[ \begin{matrix} 1 & 1 \\ 1 & 1 \end{matrix} \right]} = 0/0[/math].

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