Hey guys, I just get confused about the quiz in week 4.

The first one is question 6:

I do not know why only the columns of the full rank matrix could be consider the “span of the matrix”.

Also i understand what is the span of a linear space (i.e. 2d linear space = plane, 3d becomes 3D space), but what is the “span of a matrix”? I don’t think in the videos there is any description talking about it and gives the mathematical expression.

In addition to that, if the description is all correct (feedback description). Why is that the case that only columns are correct not the rows? Is there any difference between the matrix and its transpose in terms of the rank? Since the question is basically asking, if the rows are linearly dependent or the columns are linearly dependent.

The second question is about Q.7

I don’t think there is any correct answer, and the following is my deduction.