Use algebra as a way to introduce matrices. One of the most useful aspects of matrices is their ability to mimic numbers in an algebraic sense. Students who are at a level in which matrices are to be introduced have taken algebra and should be familiar with most algebra topics and methods.. Using this method, the teacher reviews algebra facts and properties using matrices in place of numbers. This teaching method also offers the advantage of giving the teacher an idea of what her students grasp about algebra.
Students might have difficulties visualizing matrices and their operations. This is especially true for more complicated matrices and more complicated matrix algebra. By using computer software, especially database software that can display data such as students can familiarize themselves with matrices hands-on. Examples of software that can display matrices are Microsoft Excel and the statistical software R, Computer software offers the benefit of letting students learn or practice computer software skills, which are often needed in the computation of matrix problems.
Many introductions to matrices tend to use only small matrices (2x2 and 3x3) to show students how to apply matrices to problems that could be solved without the aid of matrices.
Thus, students are left without the knowledge that matrices are infinitely more efficient than other algebraic methods. To show the actual utility of a matrix, present your students with examples that would be virtually impossible to solve using basic algebraic methods, and then show them how matrix manipulation can almost immediately solve the problem.
Many mathematics courses, especially upper-level courses, tend to view mathematics as an end in itself, not showing students how to relate the new methods to their own lives and thus students will not internalize what they have learned. Consider teaching matrices through the use of real-world problems. There are many different real-world examples for matrix theory at every level, from the solving of multiple linear equations to linear programming.