What the meaning of span space?

[neilqiqi]

1. The question goes that "Find two orthogonal vectors that span the same space as the two vectors"
The thing is, I know the definition of SPAN, say, a vector b is in span{v1, v2...vp} if x1v1+x2v2+...+xpvp = b. But what's the meaning of "span the same space"?

Homework Equations

The Attempt at a Solution

 

[Tomer]

if two sets of vectors "span the same space", it means that the new sets, spanned by these sets, are equal.
For example, sp {(1,0), (0,1)} = sp {(1,1), (1,0)}, while both of the spans are the set R^2.

In general, when you get two sets and you want to prove that they span the same space, you need to show that every element in the first span is also an element in the second span, and vice versa.
Hope it's clearer...