We primarily focus on the definitions of the linear spaces here. You have to be comfortable in all the ways you can express the four fundamental linear spaces of a matrix. Chapter 3.2 also contains how to find all \(\bf x\) such that \(A{\bf x}=0\) (ie characterize all vectors of the null space), but we will take that up in the next module.

Also note that Chapter 3.2 goes into what happens when you encounter free columns in elimination, but we already know that from the elimination module. Rather than treat elimination piece by piece, we learnt the entire procedure and all its cases (and you have written code for that) in prior modules. Note that we didn’t stop at the upper triangular matrix in the Gaussian elimination module, we went on to get to the reduced row echelon form, which is only introduced now in Chapter 3.2.