What is the most convenient way to introduce matrices to students?

[matqkks]

What is the most convenient way to introduce matrices to students?

 

[Klockan3]

Depends on what you want the students to know about matrices. An easy way is to start out with systems of linear equations and then show how to present those as matrix equations.

 

[zif.]

Show them how useful they are and then they'll do whatever's needed to learn them. Take a standard kinematics problem from first year physics that involves solving three equations simultaneously, set it up as a matrix, throw it in a TI-83 and have an answer damn near instantly.

Also balance a chemical equation, that floored a lot of people (myself included) in my intro to linear algebra class.

 

[Stephen Tashi]

This book is a cheap, thin and easy way: Matrices and Transformations [Paperback]
Anthony J. Pettofrezzo
https://www.amazon.com/dp/0486636348/?tag=pfamazon01-20

 

[Chunkysalsa]

In high school Algebra class we were shown matrices and taught how to perform basic arithmetic on them in a calculator. Thats it...

Don't do that...that was the probably like the most useless piece of information given to me in high school.

I agree that the best way is to introduce them to system's of equations. Especially when you make it into a physics or chemistry problem, really show that these objects are actually useful.

 

[matqkks]

I have seen matrices introduced as operations on vectors but you normally find this in physics books rather than mathematics ones. Is there a disadvantage in using this approach. If so what is it.
Thanks in advance.

 

[Klockan3]

I have seen matrices introduced as operations on vectors but you normally find this in physics books rather than mathematics ones. Is there a disadvantage in using this approach. If so what is it.
Thanks in advance.

Since that is the way matrices should be seen after a course in linear algebra it has merit. However unless it is done well you will likely lose a lot of students during the explanation since that is a more advanced concept than just representing systems of linear equations.

 

[Stephen Tashi]

I have seen matrices introduced as operations on vectors but you normally find this in physics books rather than mathematics ones. Is there a disadvantage in using this approach. If so what is it.
Thanks in advance.

The little book I mentioned in my previous post introduces matrices that way (as linear transformations). It doesn't require a knowledge of physics.

To me, the disadvantage of emphasizing matrices as tools for solving systems of linear equations is that systems of linear equations are boring, boring, boring. You tell kids that you will replace a haphazard disagreeable method of solving a problem with a systematic disagreeable one. Big deal!

If you are teaching computer programming as an adjunct to mathematics then I suppose the possibilities expand. Programmers appreciate systematic methods.

 

[chiro]

What is the most convenient way to introduce matrices to students?

Introducing the idea of linear transformations will help set the main idea, but as for introducing them to students, probably linear equations along with some graphical representations (like intersecting planes in R^3 for example), would probably be better to give an intuitive explanation.

Maybe explain what different kinds of linear transformations do to vectors (and maybe even other linear objects like other matrices) , and then combining that with the rest of a linear algebra sequence (vector spaces, numerical linear algebra, and so on), the students should be able to see how vector spaces and linear objects are related both in an algebraic sense and in a geometric sense (at least for simple spaces).