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.

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Example

See also

Example

In general, a system with ''m'' linear equations and ''n'' unknowns can be written as
: $a\_\{11\}x\_1\; +\; a\_\{12\}x\_2\; +\; ...\; +\; a\_\{1n\}x\_n\; =\; b\_1\; ,$
: $a\_\{21\}x\_1\; +\; a\_\{22\}x\_2\; +\; ...\; +\; a\_\{2n\}x\_n\; =\; b\_2\; ,$
:
: $a\_\{m1\}x\_1\; +\; a\_\{m2\}x\_2\; +\; ...\; +\; a\_\{mn\}x\_n\; =\; b\_m\; ,$
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 $a\_\{ij\}$ as the (''i'',''j'')-th entry:
: $$
egin{bmatrix}
a_{11} & a_{12} & cdots & a_{1n} \
a_{21} & a_{22} & cdots & a_{2n} \
dots & dots & ddots & dots \
a_{m1} & a_{m2} & cdots & a_{mn} end{bmatrix}

See also

★ System of linear equations