Monday, November 14, 2016

Gauss-Jordan Elimination

After Sputnik went up in '57, plenty of Americans worried that our education system was substandard.  How could it not be, they presumed, given that the Russkies beat us into space?  Part of the solution became known as New Math.

By the time young Darren got into elementary school in the 70s, the New Math was firmly rooted.  I recall learning about set theory and numbers in different bases--presumably, the "smart" people decided that if students learned and understood those two topics, our deficiencies in math would be over.

I didn't pay much attention to education in the 80s, I was too busy protecting America from the commie hordes.  But the 90s turned us to "fuzzy math", and the counter-swing to that in the 2000s was a "back to basics" approach.

So here we are in 2010s, Common Core-ing away, and it looks to me like the "smart" people have decided that if students learned and understood matrices, our deficiencies in math would be over.  In the past I've taught how to add and multiply matrices, and even how to use Cramer's Rule (an application of matrices) to solve systems of equations.  But today--ah, today I taught Gauss-Jordan elimination.

It doesn't matter if you know what that is or not.  What matters is that I've never taught it before, so I did plenty of prep work to ensure it went smoothly.  I even created a step-by-step worksheet that my students and I worked on together.

It went so smoothly.  Before they knew what was happening, they'd solved a 4x4 system of equations and hadn't even broken a sweat!  Such a feat would have been extremely difficult and time-consuming using algebraic elimination or Cramer's Rule, but the Gauss-Jordan algorithm made light work of it. 

It was great fun teaching something new :-)

2 comments:

Richard Clark said...

But did you use partial pivoting to improve numerical stability? :)

Darren said...

The numbers all came out nice, pretty integers. They were as stable as stable gets.