Gaussian Elimination: Planes That Swing Around a Line
An interactive live film: the three equations of the book's example are planes in 3D; each row operation swings a plane around its line of intersection with the pivot row while the solution stays fixed, until U is upper triangular.
Narration
Each equation of A x equals b is a plane in three dimensions: red for row zero, blue for row one, green for row two. The solution is the one point where all three planes meet.
Elimination replaces row one by row one minus l times row zero. Any point on both planes still satisfies the new equation, so the blue plane swings around the line where it meets the red one, and the solution point never moves.
The rest of the narration is in the book's Companion.
