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**Rapid_W** $\displaystyle

x_{1}-x_{2}+3x_{3}+2x_{4}=4

$

$\displaystyle

2x_{1}-x_{2}+3x_{3}+x_{4}=6

$

$\displaystyle

3x_{1}-2x_{2}+6x_{3}+3x_{4}=15

$

When put into rref from i get

$\displaystyle

\left(\begin{array}{cccc|c}1&0&0&-1&2\\0&1&-3&-3&-2\\0&0&0&0&5\\\hline\end{array}\right)$

Now this says 0 = 5, so presumably this system is inconsistant as 0 in my experiance doesn't equal 5.

Is there any way to find out if the system is inconsistant before i do 5 or more elementary row operations, which could be vital time wasted in an exam?

Thanks