In the previous section, we looked at solving a system of linear equations with inequality constraints. If a set of systematic linear equations has constraints that are deterministic, we can represent the problem as matrices and apply matrix algebra. Matrix methods represent multiple linear equations in a compact manner while using existing matrix library functions.

Suppose we would like to build a portfolio that consists of three securities: a, b, and c. The allocation of the portfolio must meet certain constraints: it must consist of six units of a long position in the security a. With every two units of the security a, one unit of the security b, and one unit of the security c invested, the net position must be long four units. With every one unit of the security a, three units of the security b, and two units of the security c invested...