APPLICATIONS OF SYSTEMS OF LINEAR EQUATIONS


Systems of Linear equations arise in a wide variety of applications and are one of the central themes in linear algebra.  There are mainly two applications of systems of linear equation.


Polynomial Curve Fitting

Suppose a collection of data is represented by n points in the xy-plane,

         (x1, y1), (x2, y2),.....,(xn, yn)

and you are asked to find a polynomial function of degree n - 1

          

whose procedure is called polynomial curve fitting. If all x-coordinates of the points are distinct, then there is precisely one polynomial function of degree n - 1 (or less) that fits the n points.