Finding a Basis of W: Exploring Rows & Matrices

[Dell]

given these 3 vectors

w1=(1 0 1 -1)
w2=(2 1 2 -3)
w3=(3 1 1 -2)

and i am asked to find a basis of W, subspace of R4

to do this am i supposed to put these vectors into a matrix and try elliminate rows, leaving the basis being the rows i could not get rid of??

does it matter if i put them in a "standing" matrix "A" or a "lying down" matrix "A^t "

i tried this with an A^t like matrix, but couldn't elliminate any of them,? are they all 3 the basis or have i done something wrong?

 

[Dick]

If you can't create a row of zeros by elimination, then they are linearly independent and you need them all to form a basis of their span, yes.