Dimension of a subspace question

[de1337ed]

I'm a little confused about some of the matrix terminology.
I have the following subspace:

span{v1, v2, v3} where v1, v2, v3 are column vectors defined as:

v1 = [1 2 3]
v2 = [4 5 6]
v3 = [5 7 9]
(pretend they are column vectors)

How am I supposed to find the dimension of the span?

My Work:

I created a 3x3 matrix using the column vectors, then I performed row operations to get it into upper triangular form. After performing these row operations, I ended up with the resulting matrix:
[1 4 5
0 -3 -3
0 0 0 ]

So because the rank(A) = 2, the dimension is 2. Am I right?
Also, how would I go about finding the basis vectors. Thank you.

 

[Dick]

If you are going to do row reduction put your vectors into the matrix as rows. So yes, you'll get dimension 2. The two nonzero rows will be basis vectors.