Linear Algebra lecture Part 1.1(c) - General solution = Particular solution + Homogeneous solution

Part 1.1(c) of the linear algebra lecture will show you that the description of the solution sets of linear systems fit a pattern and have a vector that is a particular solution of the system added to an unrestricted combination of some other vectors. It talks about the theorem that has 2 corresponding parts. Lastly, it explains what makes a homogeneous system consistent.

TIMESTAMPS
List of contents that was covered in the previous video 00:30
What will be covered in this video 00:40
Example of a solution set that has a vector that is a particular solution of the system added to an unrestricted combination of some other vectors 01:00
Theorem 01:30
Focusing on the unrestricted combination part of the solution set 01:40
An example of a homogeneous system having infinitely many solutions 02:00
2 lemmas used to prove the Theorem 02:20
Example of a system that illustrates the Theorem 02:30
Examples of system where the general solution set is empty 03:00
Factors affecting the size of the general solution 03:20
What makes a square matrix singular or non-singular 03:30
Summary of what we have learnt from this video 03:40
List of content we have covered so far 03:50


SUMMARY
- Describe the solution sets of systems having a unique solution, no solution at all, or infinitely many solutions
- Notation of systems of linear equations and their solution sets

Do checkout my previous video on Linear Algebra Part 1.1(b) at if you are not able to understand clearly.

Leave me a comment if you have any message.

Cheers,
Farhan

Song: Jim Yosef - Eclipse [NCS Release]
Music provided by NCS Release
Video Link:

education,homogeneous solution,linear algebra,lemma,