Coefficient matrix

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

[edit] Example

In general, a system with m linear equations and n unknowns can be written as

$a_{11}x_1 + a_{12}x_2 + ... + a_{1n}x_n = b_1 \,$

$a_{21}x_1 + a_{22}x_2 + ... + a_{2n}x_n = b_2 \,$

$\vdots \,$

$a_{m1}x_1 + a_{m2}x_2 + ... + a_{mn}x_n = b_m \,$

where $x_1,\ x_2,...,x_n$ are the unknowns and the numbers $a_{11},\ a_{12},...,\ a_{mn}$ are the coefficients of the system. The coefficient matrix is the mxn matrix with the coefficient $a i j$ as the (i,j)-th entry:

$\begin{bmatrix} a_{11} & a_{12} & \cdots & a_{1n} \\ a_{21} & a_{22} & \cdots & a_{2n} \\ \vdots & \vdots & \ddots & \vdots \\ a_{m1} & a_{m2} & \cdots & a_{mn} \end{bmatrix}$