# Thread: Finding basis test within a couple of hours!

1. ## Finding basis test within a couple of hours!

Hey guys, from what I know there are four different bases. Left Nullspace, nullspace, row space, and column space which each has their own basis. The question asks, for the following system R5, Find a basis of this subset, what is its dimensions.

[ 1 2 1 2 1 ]
[-1 -2 0 0 1]
[-2 -4 0 1 3]
[ 0 0 1 3 3 ]
[ 1 2 2 5 4 ]

Can someone explain what basis they are looking for and how to answer this question? My friend told me its just asking for the row space basis. I dont have much time!

TIA

2. Originally Posted by aeubz
Hey guys, from what I know there are four different bases. Left Nullspace, nullspace, row space, and column space which each has their own basis. The question asks, for the following system R5, Find a basis of this subset, what is its dimensions.

[ 1 2 1 2 1 ]
[-1 -2 0 0 1]
[-2 -4 0 1 3]
[ 0 0 1 3 3 ]
[ 1 2 2 5 4 ]

Can someone explain what basis they are looking for and how to answer this question? My friend told me its just asking for the row space basis. I dont have much time!

TIA
Perhaps the problem is that you have the question wrong. What you give is NOT a subspace so it makes no sense to ask for a "basis for this subset". I would interpret that as "find a basis of the subspace spanned by this subset" which would be the same as "find a basis for the row space of this matrix", interpreting each "vector" above as a row of a matrix.

In any case, since that set of vectors already spans the subspace, you just need to find an equivalent independent set of vectors. And you can do that by "row reduction" as if this were a matrix. The dimension will be the number of non-zero rows after you row reduction.