Solutions Sets of Non-Homogeneous Linear Systems

In this video, we introduce the null space of a matrix. We prove that it is a subspace of F^n and show how to find a spanning set for the null space.

Linear Algebra Done Openly is an open source linear algebra textbook developed by Dr. Andrew Misseldine. It is supported and improved by student contributions done by Math 2700 students at Southern Utah University, since Fall 2018. The textbook can be found at:

This lecture covers section 2.6 - Solution Sets from the book. This is part 3 of 3 videos from this section.

[darrenpeck]

I am looking forward to the calculus playlists to see how linear algebra and limits come together there.

[amitbisht]

Sir, so what can be said about the number of Linearly independent solutions of the given non homogeneous system. Should it be 2 Linearly independent solutions or 1. And since we know for homogeneous system of Linear equations the number of Linearly independent solutions are same as nullity or free variables i.e. 1 in this case . So can we say in general for consistent non homogeneous system with free variables the number of Linearly independent solutions are nullity + 1 (nullity becuz of free variables and +1 cuz of particular solution i.e. a constant vector)