Span, basis & linear combinations — 3Blue1Brown · Essence of Linear Algebra Ch.2

Basis vectors, span as reachable space, and linear dependence vs independence.

î = [1, 0]
ĵ = [0, 1]
v = [3, 2]
Basis vectors — î and ĵ are the standard basis. Every vector [x, y] = x·î + y·ĵ. Drag î (blue), ĵ (green), or the purple vector v.

Drag any arrowhead to move it