Linear Algebra Example Problems - Matrix Null Space Basis and Dimension

The null space of a matrix is the collection of all vectors such as Ax = 0. In this video we show how to to find a basis to describe this subspace.

Simply perform row operations on A to obtain a reduced echelon form of the matrix to identify the basic and free variables in the system. Then, write this solution as a linear combination of free variables times a vector. These vectors are the basis of the null space and the number of vectors is the dimension of the space.

[cosmicangel]

Yes. This is literally exactly what I needed.

[Thefakisgoinon]

9 minutes of this video is better than 4hours worth of lectures in university

[danielvanbibber]

This is the clearest explanation on this subject I have seen thus far! Thank you!

[gauravbadhani]

Great...after 2 hrs i have exam...this helped a lot easy explanation...thanks a lot...

[mariettarandolph]

Sorry, at timestamp 4:43. Multiplying A by <x1, x2, x3.x4, x5> = <0, 0, 0, 0>. Correct? Forgot to mention that your Linear Algebra videos are by far the best!!

[password]

These videos are some of the best linear algebra content avialable on the internet

[backtonature]

thanks a lot sir, you are better than my teacher at my university.

[Zuwwar]

You are a blessing and a great teacher

[phuclehoang]

thank you a lot sir. You make it easy for student to understand.

[SpitfireAce]

Perfectly explained! Exactly what I needed.

[MegaDurocher]

I appreciate you filling in the missing steps from my math notes

[nickyeung]

Just love your teaching videos, Adam!!! I’m a math teacher too, I’m wondering what software / app you’re using in your explanation? It looks so smooth during your teaching!! May I know it ? Thank you very much . 🙏

[DarknessIsThePath]

I learned what nullspace and dimension is in 9 min than I did in 1 week lol, excellent video!

[suryat]

Excellent Explanation.
Keep up good work.
Thanks
Surya

[prospermukura]

Great teacher indeed...this video eradicated my confusion on this topic...thank you

[baphomet]

Thank you so much. It was of great help. Could you please recommend some reference books on this topic?

[ashrule]

great video, very clear explanation. thanks!

[marufbillah]

You are a blessing and a great teacher. tnx a lot <3

[fenerbahcesk]

if there is no free variable so if all row has pivot what will we do what is the dimension of nullspace

[cathylin]

Do we need to check whether these 3 vectors are linearly independent?