How do we find the set of vectors that are in the row space of A?
Do we do this by row reducing the following matrix?
(1 3 | 0)
(1 0 | 0)
(2 1 | 0)
The row space of a matrix is the space spanned by its rows. If this matrix has two linearly dependent rows (and it does) then as the rows are 2-vectors the row space is either R^2 or C^2 depending on if we are dealing with real or complex spaces/matrices.
You are in a Linear Algebra class, already done that, it is fundamental to know and still not know it. Further you have a textbook which gives the definitions!
I don’t think that this in a traditional “Linear Algebra” class.
There are “classical matrices” classes.
In these ‘linear independence’ is not a topic.