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Mathematics-Online course: Linear Algebra - Linear Systems of Equations - Classification and General Structure

Linear System of Equations

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A linear system of equations (LSE) over a field $ K$ is given by

$\displaystyle \begin{array}{ccccccc} a_{1,1}x_1 & + & \cdots & + & a_{1,n}x_n ... ... & + & a_{m,n}x_n & = & b_m \end{array} \quad \leftrightarrow \quad Ax = b $

with coefficient matrix $ A = (a_{i,j})\in K^{m\times n}$, 'unknown' $ x\in K^n$ and right hand side $ b\in K^m$.

The LSE is called homogeneous if $ b = 0$. Otherwise it is called inhomogeneous.

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  automatically generated 4/21/2005