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

Gauss Elimination for an invertible Matrix

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By Gaussian elimination any LSE with invertible $ n\times n$ coefficient matrix $ A$ can be brought to upper triangular form in at most $ n-1$ steps. For this purpose all coefficients below the diagonal are successively nullified, that is, after $ \ell-1$ steps the LSE has the form


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

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  automatically generated 1/9/2017