Linear Algebra › Section A · Linear equations in linear algebra › Topic A.7
Span and linear independence
Span asks what a set of vectors can build; linear independence asks whether every vector in the set is really needed. Together they decide how many directions a set of vectors truly covers, and both are settled by counting pivots.
In this topic
- Two questions about a set of vectors
- Span, revisited
- Linear independence
- Worked example: finding a dependence relation
- Sets of one or two vectors
- What dependence really means
- Two shortcuts
- Span and independence together
- Worked example: independent and spanning
- Common mistakes to avoid
- Key takeaways
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