en>Rjwilmsi: ISBN error fixes, Changed 0-201-53082-1. using AWB (9877)

2014-01-23T11:47:32Z

ISBN error fixes, Changed 0-201-53082-1. using AWB (9877)

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{{Unreferenced|date=December 2009}}

In [[linear algebra]], the '''coefficient matrix''' refers to a matrix consisting of the coefficients of the variables in a set of [[linear equations]].

==Example==
In general, a system with ''m'' [[linear equations]] and ''n'' unknowns can be written as
: <math>a_{11}x_1 + a_{12}x_2 + \cdots + a_{1n}x_n = b_1 \,</math>
: <math>a_{21}x_1 + a_{22}x_2 + \cdots + a_{2n}x_n = b_2 \,</math>
: <math>\vdots \,</math>
: <math>a_{m1}x_1 + a_{m2}x_2 + \cdots + a_{mn}x_n = b_m \,</math>

where <math>x_1,\ x_2,...,x_n</math> are the unknowns and the numbers <math>a_{11},\ a_{12},...,\ a_{mn}</math> are the coefficients of the system. The coefficient matrix is the ''mxn'' matrix with the coefficient <math>a_{ij}</math> as the (''i'',''j'')-th entry:
: <math>
\begin{bmatrix}
a_{11} & a_{12} & \cdots & a_{1n} \\
a_{21} & a_{22} &\cdots & a_{2n} \\
\vdots & \vdots & \ddots & \vdots \\
a_{m1} & a_{m2} & \cdots & a_{mn} \end{bmatrix}
</math>

==See also==
* [[System of linear equations]]

{{DEFAULTSORT:Coefficient Matrix}}
[[Category:Linear algebra]]

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en>Rjwilmsi: ISBN error fixes, Changed 0-201-53082-1. using AWB (9877)