The Relationship Between Systems Of Equations and Matrices

I don't know about any other teachers but I still teach systems of equations separately from matrices because I learned them as two separate entities. It wasn't until years later I learned about their connection.

Even now, I have to make a conscious decision to connect the two topics in Algebra II or I end up treating them as unrelated.  So this year, after I finish teaching solving systems of two equations by graphing, substitution, and elimination, I plan to slip in enough matrices for them to solve systems of equations with two and three equations.

First step is to have students become proficient or at least reasonable at solving systems using both substitution and elimination because both skills are used while working with matrix.  Instead of moving on to systems of inequalities, I'm going to have them learn the basics of matrix math.

From here its a hop, skip, and, jump to learning more about matrices and learn enough to easily solve a system of three equations.  This will be like building a good building after laying a strong foundation.  In a sense its like long division versus synthetic division, one method can take more time to do than the other.

So when is using matrices better than using systems of equations to solve a problem better or is there?  Well I spoke with a computer programmer and asked him.  His answer was an emphatic matrices because those are easier to program than systems of equations.  In addition, matrices are used in computer graphics any time there you see light going through water.  This is because the science used in optics to account for reflection and refraction is another use of matrices.

Furthermore, matrix math is used in calculating the electrical properties of a circuit, volts, amps, resistance, and other aspects.  Matrix math is also used in electrical engineering to give approximations of more complicated equations. 

In some circumstances matrices represents data while in others it represents equations. Some IT companies use data matrix to track all sorts of user information, carry out search requests, and help manage databases.  Furthermore, geologists use matrix to carry out seismic surveys, and plotting graphs.  In other fields, matrices allows calculations for optimization problems.  In robotics matrices are used to direct its movement. 

This is important because students like to know how to relate the current topic to the real world.  If they do not see a reason for learning the topic, they are less likely to want to learn it.  So know, I have the beginnings of the answer to "Why do I need to learn this?" and perhaps they will be more willing to learn it.