Back Substitution: A Plane, a Line, a Point
An interactive live film: in an upper triangular system each row brings one new unknown, so the last row is a flat plane, the next meets it in a line and the first cuts the line at the solution; set a diagonal entry to zero and the planes never meet.
Narration
Gaussian elimination has made this system upper triangular: U x equals c. Each row is a plane, the red one, the blue one, and the green one, and the solution is where all three meet.
Start with the last row. It has only one unknown, x two, so the green plane lies flat, at height one. That pins x two equals one.
The rest of the narration is in the book's Companion.
