Examples:

1. Is the below linear system redundant or inconsistant?

   1.2x + 1.4y + 5z = 4.05
1.92x + 2.24y + 8z = 6.48
3.84x + 4.48y + 12z = 10.96

   The above system is redundant in respect to equations one and two. This is because line two is equal to line one multiplied by 1.6.

2. $\left(\begin{array}{cccc}1.2& 3.0& 4.6& 1.2\\ .61& -1.4& .22& .4\\ .48& 1.2& 1.84& .48\\ 1.22& -2.8& .11& 1.2\end{array}\right)*\left(\begin{array}{c}a\\ b\\ c\\ d\end{array}\right)=\left(\begin{array}{c}34.98\\ .8760\\ 13.992\\ 2.8060\end{array}\right)$

   The above system does not have unique solutions due to redundency of the first and third equation sets by a factor of 2.5.