Mortality for Sets of 2 × 2 Matrices

Do undergraduate mathematics majors know much about what has been discovered in mathematics during this century? One such concept, blossoming in the 1930s, is the theory of solvability. A problem is said to be solvable if there exists a decision procedure, or algorithm (i.e., a defined procedure for solving a problem using a finite number of steps), that will yield a solution to the problem. The purpose of this paper is to give some examples of open solvability problems and to demonstrate the solution to another. This material is accessible to a first-semester linear algebra student. To more easily understand some of the concepts to follow, consider the following set of 2 X 2 matrices: