# solution sets of linear systems

(1.7 hours to learn)

## Summary

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.

## Context

This concept has the prerequisites:

- linear systems as matrices
- column space and nullspace (The column space and nullspace help determine the solution set.)

## Core resources (read/watch one of the following)

## -Free-

→ 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)

## -Paid-

→ 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

Additional dependencies:

- Gaussian elimination
- computing the nullspace

## See also

-No Additional Notes-