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Mathematics-Online course: Preparatory Course Mathematics - Linear Algebra and Geometry - Systems of Linear Equations

Gauss Elimination to Echelon Form

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By Gaussian elimination any LSE can be brought to row-echelon form:

$\displaystyle Ax = b \rightarrow
\left(\begin{array}{cccc ccc}
\left(\begin{array}{c} c_1 \\ \vdots \\ c_m

where the so called pivots

$\displaystyle p_1=a'_{1,j_1},\ldots,p_k=a'_{k,j_k},\quad
1\le j_1<\cdots<j_k\le n\,

are not equal to zero and $ k$ is the rank of $ A$.

In detail the $ \ell$-th elimination step proceeds as follows:

(Authors: Burkhardt/Höllig/Streit)

(temporary unavailable)

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  automatically generated 1/9/2017