Have you ever heard of a matrix kernel or nullspace? If not, or you’d like a refresher on the topic, keep reading! We’re doing a Maple Learn document walkthrough today on Fundamental Subspaces.

The document starts by defining the nullspace/kernel and nullity of a matrix. Nullity is defined as the number of vectors in the basis of the kernel for the given matrix. This makes sense, as nullspace is defined as:

This may still not make sense to you, and that’s okay! We have an example for a reason, where we try to find a basis for Null(A) and state the dimension of the subspace (nullity).

I won’t go through the solution here, as trying it yourself is always important. But one hint! If you get really stuck, you can find the Reduced Row Echelon Form (RREF) and the kernel using Maple Learn’s context panel, or check out the rest of our Matrices collection for other helpful documents on this topic.

Please let us know what you thought of this walkthrough or if there are any specific documents or topics you’d like to see in the comments below this post. I hope you enjoyed this walkthrough!