$\operatorname{Span}(T) = \operatorname{Span}(T - \{v\})$ Please help : We've been given homework to do problems on vector spaces and I came across one question that I got stuck on.
How do I find the $\operatorname{Span}(T)$ given that $T =\{(1,0,2),(0,-1,1),(1,1,1)\}$? I know the according to the plus/minus theorem $\operatorname{Span}(T) = \operatorname{Span}(T - \{v\})$. I'm not really sure if I should minus one vector from the set of vectors and then find the span of the result I get but then which vector do I choose to subtract from the 3? 
 A: Notice that if you add the las two vector you get the first vector, and the last two are linearly independent (look at the first component of both), which means that the span is given by...
Can you conclude?
Leave a comment if not.
A: Hint You have three vectors $(1, 0, 2), (0, -1, 1), (1, 1, 1)$.


*

*Subtract the first vector from the third vector.

*Add the third vector to the second vector.
You should  be left with three vectors, and the second vector should be zero.  Then all linear combinations of the three vectors are given by $\alpha$ times the first vector, plus $\beta$ times the third vector.  The resulting span should be all vectors of the form
$$
(\alpha, \beta, [\text{some expression in terms of } \alpha \text{ and } \beta]).
$$
A: What you need to do is put the vectors in columns and find the reduced row echelon form of the Matrix that you formed. 
Example: After you get the rref(A) where columns of A contain all the vectors in the given set. You'll get:
1 0  1
0 1 -1
0 0  0
which you can conclude that the third vector is a redundant vector. First and second vector is enough to span T. By the plus/minus theorem, you can get rid of the third vector and still having the same span. Hope it helps.
