The matrix you row reduced tells you that one of your vectors is dependent on the others. Find and remove this vector. The remaining vectors should be linearly independent, and by definition they span their span...
Find a basis of the subspace of spanned by the following vectors:
4 3 -7 10
6 14 -20 34
1 -4 3 -7
1 -4 4 -7
i turned it into a matrix and then row reduced it and got this:
1 0 1 0 0 1 -1/2 0 0 0 0 1 0 0 0 0
im just unsure what to do now, please help.
The matrix you row reduced tells you that one of your vectors is dependent on the others. Find and remove this vector. The remaining vectors should be linearly independent, and by definition they span their span...