Unit 2: Linear combinations, span, and basis vectors
About this unit
A linear combination adds scaled vectors; the span is everything you can reach that way, and a basis is a set of independent vectors whose span is the whole space.
By the end, you can: Read coordinates as amounts of basis vectors, find the span of two vectors, and decide whether a set of vectors is a basis.
Modules
5 modulesLearn
- Coordinates are recipesArticle · A vector's coordinates are the amounts of the standard basis vectors î and ĵ; any sum of scaled vectors is a linear combination.Not started
- Span, dependence and basesArticle · The span of two vectors is the plane, a line or the origin; dependent vectors add nothing new; a basis is an independent set that spans.Not started
- Make the span collapseExperiment · Drag one vector until the pair spans only a line, and see that this happens exactly when one is a multiple of the other.Not started
- Reaching every pointReview · Linear combinations, span, independence and bases in one place.Not started