A sample of novel verbal problems which can be solved by using systems of linear equations with free variables is presented. The procedure of Gaussian elimination is used to solve the system. (KR)

Several ways to present two theorems (concerning a square matrix and a property of prime numbers) are demonstrated. One way for each theorem is more stimulating, better setting the stage for the proofs. Several methods of presenting proofs are illustrated, with the outcomes considered from the learner's viewpoint. (MNS)

Examples for determining the equation of a line through two points or a quadratic function that contains three noncollinear points are presented. (MNS)

A variety of examples are given from different areas of biology to illustrate the general applicability of matrix algebra to discrete models. These models of biological systems are concerned with relations between processes occurring in discrete time intervals. Diffusion, ecosystems, and different types of cells are modeled. (KR/Author)

Contends that, although the operant approach to psychology is based on objective empirical observations, much of psychology is filled with subjective, interpretive terminology. Argues that such terminology produces confusion over the definitions of basic operant concepts. Suggests a solution that defines the concepts of positive and negative…

Discusses representations in the context of solving a system of linear equations. Views representations (concrete, tables, graphs, algebraic, matrices) from perspectives of understanding, technology, generalization, exact versus approximate solution, and learning style. (KHR)

Presents a short study of proper values of two-by-two matrices with real entries. Gives examples of symmetric matrices and applications to systems of linear equations of perpendicular lines intersecting at the origin and central conics rotated about the origin to eliminate the xy term from its equation. (MDH)

The purpose of this series is to provide instructional ideas and materials that support implementation of the Curriculum and Evaluation Standards in local settings. This book addresses in a very practical way the content, pedagogy, and pupil assessment dimensions of reshaping school mathematics. Chapters include discussions and activities that…

Discussed is the use of magic squares as examples in a first year course in linear algebra. Four examples are presented with each including the proposition, the procedure, and a proof. (KR)

This is the instructor's guide to a text designed for the contemporary business student who frequently questions the need for studying mathematics. The text material is presented in a "building-block" fashion, with skills learned in earlier chapters organized to provide a smooth transition into more difficult topics. This guide consists…

Presented is a method where a quadratic equation is solved and from its roots the eigenvalues and corresponding eigenvectors are determined immediately. Included are the proposition, the procedure, and comments. (KR)

Game theory is appropriate as a topic for an honors seminar for high school students. Matrices provide a model for analyzing certain situations involving conflict, and probability theory can be used to determine the best strategies for the players. Variations on the ancient game of morra are discussed. (MNS)

That the principal axis theorem does not extend to any finite field is demonstrated. Presented are four examples that illustrate the difficulty in extending the principal axis theorem to fields other than the field of real numbers. Included are a theorem and proof that uses only a simple counting argument. (KR)

Abstract ideas in linear algebra are illustrated at different levels of difficulty through the investigation of the solution to a well-known puzzle. Matrices are used to model the puzzle and the concepts of rank, underdetermined systems, and consistency are employed in the solution to the problem. (MDH)

Included in this column are Star Trek, a geometric construction problem; a simplified approach to correlation using scattergrams; a calculus problem concerning second derivatives for extreme values; and a note on integration by parts. (MNS)