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My question is concerned with vectors, null space, solving for independence and subspaces.

Now, I've found If a question gives a set of vectors and asks find if they are independent or not The vectors are written in columns (to make a matrix) and then Gaussian elimination is applied.

But in questions like solving for a null space (Ax=0) or subspaces the vectors are written across rows.

Yeah, The notes from my lectures are a bit funny, they seem to switch between writing vectors along columns or rows quiet regularly. If anyone has some general rules about when to write vectors either way, I'd be very grateful.

(If anyone tries to explain something with a diagram/matrix I'd prefer it to be done with 3 vectors in 4 dimensions. Sorry for being fussy but I think because this is a question about the uncertainty of columns/row I'd think it would be best.)

Thanks!