No new commands here, but instead we can now reveal and explore one of our Sage mysteries. When we create a null space with .right_kernel(basis='pivot'), or a span with .span(), Sage internally creates a new spanning set for the null space or span. We see the vectors of these spanning sets as the rows of the Basis matrix or User basis matrix when we print one of these sets.
But more than a spanning set, these vectors are always a linearly independent set. The advantages of this will have to wait for more theory, but for now, this may explain why the spanning set changes (and sometimes shrinks). We can also demonstrate this behavior, by creating the span of a large set of (linearly dependent) vectors.
So the above examines properties of the two vectors, S, that Sage computes for the span W built from the seven vectors in the set L. We see that the span of S is equal to the span of L via the comparison X == W. And the smaller set, S, is linearly independent, as promised. Notice that we do not need to use Sage to know that L is linearly dependent, this is guaranteed by Theorem MVSLD.