Given that we have 5 vectors and we want to find which 4 spans R^4. May i know what is the difference if i express the vectors as column vectors as compared to if i express them as row vectors and then perform row operations?
i did it as column vectors but the answer in my notes expresses the vectors as row vectors.
keep in mind that when dealing with bases, they aren't unique. what remains invariant (and what is the important piece of information) is the size of the basis, that is, the dimension of the spanned space.
row-space is like a "mirror-image" of column space. for example, if you are supposed to use columns, but you prefer to use rows, work with the transpose of a given matrix, then transpose back when you're finished, and no one will ever know....