How do I determine if a system of linear equations is consistent or inconsistent without solving the matrix?
For example: $$\left[\begin{matrix}2 & 0 & 0 & -4 & -10 \ 0 & 3 & 3 & 0 & 0 \ 0 & 0 & 1 & 4 & -1 \ -3 & 2 & 3 & 1 & 5\end{matrix}\right]$$

Question

How do I determine if a system of linear equations is consistent or inconsistent without solving the matrix?
For example: $$\left[\begin{matrix}2 & 0 & 0 & -4 & -10 \ 0 & 3 & 3 & 0 & 0 \ 0 & 0 & 1 & 4 & -1 \ -3 & 2 & 3 & 1 & 5\end{matrix}\right]$$

anonymous · Answer

I know what consistent and inconsistent are and I have solved several matrices now, but this question seems odd to me. Are there some signs I should be able to observe just from eyeballing this to give it away?

anonymous · Answer

Any suggestions, links or tips? :D

anonymous · Answer

If it looks like you can get the matrix down to reduced row echelon form, it's consistent.  If you don't think you can get to that form, it's inconsistent.  That would be the easiest way to just eyeball it and guess.