Mo logo [home] [lexicon] [problems] [tests] [courses] [auxiliaries] [notes] [staff] german flag
Mathematics-Online course: Preparatory Course Mathematics - Linear Algebra and Geometry - Systems of Linear Equations

Solution of a Linear System of Equations in Echelon Form

[previous page] [next page] [table of contents][page overview]
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)

(temporary unavailable)
[previous page] [next page] [table of contents][page overview]
  automatically generated 1/9/2017