Linear Algebra › Section A · Linear equations in linear algebra › Topic A.3
Vectors and vector equations
A column of numbers can be treated as a single object that you add, scale and picture as an arrow. Seeing a linear system as one equation between vectors turns solving into a geometric question: can this target be built from these ingredients?
In this topic
- One object, many numbers
- Vectors in the plane
- The geometric picture
- Vectors in R³ and Rⁿ
- Linear combinations
- Vector equations are linear systems
- Worked example: finding the weights
- The span of a set of vectors
- Worked example: a vector outside the span
- Common mistakes to avoid
- Key takeaways
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