Coefficient matrix

From Wikipedia, the free encyclopedia

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

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

This article is issued from Wikipedia. The text is available under the Creative Commons Attribution/Share Alike; additional terms may apply for the media files.