solution sets of linear systems
(1.7 hours to learn)
The set of solutions to Ax = b can be characterized in terms of the column space and nullspace of A. If b is in the column space of A, then a solution exists, otherwise not. The full set of solutions is given by any particular solution x0, plus the nullspace of A.
This concept has the prerequisites:
Core resources (read/watch one of the following)
→ MIT Open Courseware: Linear Algebra (2011)
Videos for an introductory linear algebra course focusing on numerical methods.
Supplemental resources (the following are optional, but you may find them useful)
→ Introduction to Linear Algebra
An introductory linear algebra textbook with an emphasis on numerical methods.
Location: Section 3.4, "The complete solution to Ax = b," pages 155-160
- Gaussian elimination
- computing the nullspace
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