1. ## [SOLVED] Understanding Spanning

Hey guys.

I have a simple question regarding spanning.

Obviously, if V = {( $e_1, e_2, e_3, e_4$) | ( $e_1, e_2, e_3, e_4$) $\in R^4$}
V spans $R^4$.

Can I say that V spans $R^3$??

2. Originally Posted by jayshizwiz
Hey guys.

I have a simple question regarding spanning.

Obviously, if V = {( $e_1, e_2, e_3, e_4$) | ( $e_1, e_2, e_3, e_4$) $\in R^4$}
V spans $R^4$.

Can I say that V spans $R^3$??

Of course not: $\mathbb{R}^3$ is not even a subset of $\mathbb{R}^4$ and thus no element of V is contained in it!

Tonio

3. Originally Posted by tonio
Of course not: $\mathbb{R}^3$ is not even a subset of $\mathbb{R}^4$ and thus no element of V is contained in it!
So basically,

(1,0,0,0) $\in R^4$

but

(1,0,0) is never $\in R^4$.

Is it possible do draw a vector with 2 components in a three dimensional space?

and vice versa,

can you draw (1,0,0) in a two-dimensional plane???

4. Originally Posted by jayshizwiz
So basically,

(1,0,0,0) $\in R^4$

but

(1,0,0) is never $\in R^4$.

Is it possible do draw a vector with 2 components in a three dimensional space?

and vice versa,

can you draw (1,0,0) in a two-dimensional plane???
In $\mathbb{R}^2$, vectors are of the form $(x,y)$; therefore, how can a vector of the form $(x,y,z)\in\mathbb{R}^2$?

5. In , vectors are of the form ; therefore, how can a vector of the form ?
I dunno. But I would assume a two-dimensional plane (1,3) would be found in the (x,y) plane of (x,y,z) space...

In everyday life, we live in three-dimensional space containing two-dimensional things...Unless you count time as a 4th dimension...But let's not digress...

6. Originally Posted by jayshizwiz
I dunno. But I would assume a two-dimensional plane (1,3) would be found in the (x,y) plane of (x,y,z) space...

In everyday life, we live in three-dimensional space containing two-dimensional things...Unless you count time as a 4th dimension...But let's not digress...
(1,3) Is not the same as (1,3,0)

7. Gotcha,
Thanks.