Span & Bases

What can two vectors reach?

An interactive lesson with 6 steps, about 5 minutes: you predict, drag and solve, with instant feedback on every answer. It runs in your browser and needs JavaScript.

What you’ll learn

• A linear combination is $a\mathbf u + b\mathbf v$. The span is everything you can reach.
• Two vectors on the same line are dependent: their span is just a line.
• Two independent vectors in the plane form a basis: every point has unique coordinates.

Steps

1. Linear combinations
2. Reach the target
3. Pointing the same way
4. Bases
5. A line, not a plane
6. New coordinates