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Solution of a LSE in Echelon Form

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A LSE in row-echelon form

$\displaystyle \left(\begin{array}{cccc ccc} 0\ldots0 & p_1 & *\ldots* \\ & 0... ...}\right) = \left(\begin{array}{c} c_1 \\ \vdots \\ c_m \end{array}\right) $

with pivots $ p_1,\ldots,p_k$ has a solution if and only if $ c_{k+1}=\cdots=c_m=0$. The solution is unique if $ k=n$. For $ k<n$ there are $ n-k$ linearly independent solutions of the homogeneous LSE ($ c_i=0$).
(Authors: Burkhardt/Höllig/Streit)

Example:

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  automatically generated 3/16/2005