Coefficient matrix

In linear algebra, the coefficient matrix refers to a matrix consisting of the coefficients of the variables in a set of linear equations. The matrix is used in solving systems of linear equations.

Coefficient matrix

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

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

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

$\vdots \,$

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

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 $a_{ij}$ as the (i,j)-th entry:^[1]

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

References

1. Liebler, Robert A. (December 2002). Basic Matrix Algebra with Algorithms and Applications. CRC Press. pp. 7–8. Retrieved 13 May 2016.