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Equations Matrix.

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.


Source: [1].


See also: Matrix (over body K).

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