How to Solve a Kirchhoff's Rules Problem - Matrix Example
Channel: Jesse Mason
Date: 2012-04-10

ROW REDUCE LIKE DR SEUSS: 
Oh, all those numerous and nasty equations!
All the plugging and chugging, it takes too much patience.
I've got just the thing for such an awful occasion:
It's mighty, it's sleighty! It's Gauss-Jordan Elimination!
 
First, our equations enjoy preparation.
Each variable is queued in ascending gradation.
Once aligned and accounted, their nice numeral agents,
Get bumped to a matrix in corresponding locations.
 
Next, we apply a few matrix operations:
Addition and subtraction. Division, multiplication.
Yes, our rows are massaged with arithmetication,
Until they're reduced to the simplest notation.
 
Lo', all of our multiplex math manueveration,
Concludes with a comely, concise configuration.
The name of this sexy and subtle sophistication?
She goes by Row Reduced Echelon Formation.
 
To the left: a delightful diag-one-alation.
To the right: our solutions, in column notation. 
Such a time-saving tool! Such a cool calculation!
It's mighty, it's sleighty! It's Gauss-Jordan Elimation!

My video on solving equations with a matrix: http://www.youtube.com/watch?v=I134Xk4521k