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.

Example[edit]

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:


\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}

See also[edit]