if we consider following equations set (1), written informally as:
a1,1x1 + a1,2x2 + ... + a1,nxn = b1
a2,1x1 + a2,2x2 + ... + a2,nxn = b2
am,1x1 + am,2x2 + ... + am,nxn = bm
we can say:
- it is set of m linear equations with n unknown values.
- numbers ai,j ∈ K we call coefficients of that set,
- bi are free values,
- xj are unknown values.
let's use following notation:
- A = (ai,j) ∈ Km,n,
- vector b = (bi) ∈ Km,
- vector x = (xj) ∈ Kn.
then equation set (1) we can write as Matrix Equation:
A ∗ x = b.
See also: Matrix (over body K).