Linear algebra

A general type of mathematical problem arising often in chemistry is that of solving a set of simultaneous equations for more than one unknown. Most such problems of a particular, fairly simple form can be solved by the methods of linear algebra. The term "linear" refers to the fact that, for a two-variable problem, only constants and terms in x and y (the two unknowns) appear in the equations, and there are no terms containing x², xy, y², nor are there any other higher power polynomic terms. An appraoch called matrix algebra , illustrated below for the simple case of two equations in two unknowns, allows a general solution to the problem of m linear equations in n unknowns (for m > or = n).

Examples of problems the matrix method can be applied to arise in analytical chemistry. The use of absorbance measurements at two wavelengths to determine the concentrations of two components of a solution can be treated as an example of a problem of solving a system of two linear equations in two unknowns.