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.

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

where ${\displaystyle x_{1},\ x_{2},...,x_{n}}$ are the unknowns and the numbers ${\displaystyle a_{11},\ a_{12},...,\ a_{mn}}$ are the coefficients of the system. The coefficient matrix is the mxn matrix with the coefficient ${\displaystyle a_{ij}}$ as the (i,j)-th entry:

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