Linear Algebra › Section A · Linear equations in linear algebra › Topic A.4
The matrix equation Ax = b
Multiplying a matrix by a vector packs a whole linear system into one short equation. That single idea links three ways of seeing the same problem and tells you when a system can be solved for every right-hand side.
In this topic
- One equation for a whole system
- Defining the product Ax
- The row-vector rule
- Three views of one problem
- When every b has a solution
- Worked example: testing every right-hand side
- Linearity of the product
- Worked example: a parabola through three points
- Sensitive systems
- Common mistakes to avoid
- Key takeaways
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