Question

Which of the following sets are identical in R3? [I WANT TO KNOW HOW TO TELL IF THEY ARE IDENTICAL]
A. span{(1,0,1);(2,0,2)}
B.span{(1,0,1);(1,0,-1)}
C.span{(1,0,1);1,1,1)}
D.span{(3,0,3)}
E.span{(1,0,1);(2,0,2)}

Answer 1

Is there a vector missing for (D)?

Answer 2

No, I SKIPPED THE CLOSING BRACKET

Answer 3

No need to yell :P

Answer 4

HA HA HA

Answer 5

I don't think any of these answers work... I'm pretty sure you need at least three vectors for a set to span \(\mathbb{R}^3\), not to mention be equivalent to \(\mathbb{R}^3\).

Answer 6

what do they mean "identical"? I am getting your point though

Answer 7

It sounds like you want to be able to show that the span of a certain set of vectors contains every vector in the given space. So in other words, you want to be able to show that the linear combination of the vectors can represent any vector in the space.

There are a few methods for this. I don't remember all of them, but I've seen a link that lists a neat and comprehensive set of methods. Just a sec...

Answer 8

Oh, one more thing: the span of the set has to contain a basis (or maybe it was the standard basis?) of the given space in order for the set to be identical to the space.

Here's the link: http://math.stackexchange.com/questions/56201/how-to-tell-if-a-set-of-vectors-spans-a-space

Answer 9

ok thanks. let me check it out