One Vector In, One Vector Out

You'll learnto treat a matrix as a function: one vector in, one vector out.

Topic 4.12 watched the whole plane move at once. Here a matrix is a function: feed it one vector and it hands back exactly one, by the same rule every time. That single-input view is what lets sums pass straight through it and lets two machines chain into one — the behaviour this topic reasons about.

8 STEPS · 6 QUICK CHECKS · MACHINE · COLUMNS · LINEARITY · COMPOSITION · v3

Unit 4 is not assessed on the AP exam; schools include it where local requirements ask.

columns are destinations

Before you start

What you're looking at

A single input vector entering and one output vector coming out.

The question

What does this matrix do to one specific vector?

Watch for

Reasoning about the matrix as a function's behavior — the operation view, distinct from watching the whole plane move.

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