<p><it>Abstract—</it> This paper introduces an assertion scheme based on the <it>backward error analysis</it> for error detection in algorithms that solve dense systems of linear equations, $<tmath>A\mbi{x} = \mbi{b}</tmath>$. Unlike previous methods, this Backward Error Assertion Model is specifically designed to operate in an environment of floating point arithmetic subject to round-off errors, and it can be easily instrumented in a Watchdog processor environment. The complexity of verifying assertions is $<tmath>O(n^2)</tmath>$, compared to the $<tmath>O(n^3)</tmath>$ complexity of algorithms solving $<tmath>A\mbi{x} = \mbi{b}</tmath>$. Unlike other proposed error detection methods, this assertion model does not require any encoding of the matrix $<tmath>A</tmath>$. Experimental results under various error models are presented to validate the effectiveness of this assertion scheme.</p>