Can some please explain to me why [math]\{a + b + c = 0 | a,b,c \in R^3\}[/math] is a vector space but [math]\{a + b + c = 1 | a,b,c \in R^3\}[/math] isn't?

And how do I get the {} to show up?

"{" = "\{" in TeX.

 

I don´t understand your equations. What is "1"? A unit vector?

Because there's no zero vector in [math]

\{a + b + c = 1 | a,b,c \in R^3\}

[/math]? Could be wrong tho...

You understand what "a+b+c=1 for a,b,c in R³" means? What?

The set of all unit vectors that one can get by adding up three vectors in R^3?

Somehow i thijnk that it ought to be

 

{(a,b,c) in R^3:a+b+c=1}

 

is not a vector space. The thing you're written down doesn't make any sense since 1 is not in R^3

It's not a VS because there's no 0 vector? Just wondering, new to this stuff.

 

EDIT: I mean matt grime's VS.

look at the definitions and have some faith in you ability (since the answer is correct)

Yeah, it was suppose to be the vector a b c is a subset of R³...

But I got it! Thanks!

Tnx!!