I have a more simple problem, but my answer is wrong according to my book.

Find a basis for, and the dimension of, the solution space of Ax=0.

A is a matrix of rows:

1 2 -3

2 -1 4

4 3 -2

I have reduced this to row-echelon form and I get:

1 2 -3

0 1-2

0 0 0

Then, I know that the Rank(A) is 2.

columns=rank+nullity. Then, the nullity is 1.

Now, how can I have a nullity or dimension of the Nullspace to be 1, when I have two rows that are the basis. Namely, (1,2,-3) and (0,1,-2).

Thank you.