ABSTRACT
The algebra to be studied is called linear because graphs and sketches giving geometrical interpretation or illustration are composed of straight lines. The mathematical analysis is developed on the assumption that social scientists are dealing with continuous variables which can take on positive or negative values. Often the usual mathematical analysis in terms of continuous variables may give an adequate approximation; at the end of the calculation, any non-integer values can be rounded to the nearest integer. Linear systems are very useful in analysing many problems in economics and other social sciences, and in carrying out statistical estimation. This is very fortunate because it turns out that both theoretical analysis and numerical calculation are much simpler for linear than for nonlinear models. Inequalities are met in both linear and non-linear algebra. Linear inequalities occur frequently, especially in applications in social sciences contexts.
