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.
Author: Gilbert Strang

Supplemental resources (the following are optional, but you may find them useful)


See also

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