Mistake Master
Mistake Master · AP Precalculus · Unit 4 · Step-Through Animation
The Plane Moves, All at Once
You'll learnto watch a matrix move the whole plane by moving its two basis vectors.
A 2 by 2 matrix is not a grid of numbers waiting to be multiplied. It is a machine that picks up the entire plane and sets it down somewhere else, and its instruction set is written in plain sight: the two columns are exactly where the basis vectors land. Twelve short steps; press Next for each one.
Unit 4 is not assessed on the AP exam; schools include it where local requirements ask.
the columns are where the two basis arrows land
Before you start
What you're looking at
A square grid on the plane, with two colored basis arrows about to be moved by a matrix.
The question
Where do (1, 0) and (0, 1) land, and what does the rest of the plane do?