# [SOLVED] Understanding Spanning

#### jayshizwiz

Hey guys.

I have a simple question regarding spanning.

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

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

#### tonio

Hey guys.

I have a simple question regarding spanning.

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

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

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

Tonio

• dwsmith

#### jayshizwiz

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

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

but

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

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???

#### dwsmith

MHF Hall of Honor
So basically,

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

but

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

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 $$\displaystyle \mathbb{R}^2$$, vectors are of the form $$\displaystyle (x,y)$$; therefore, how can a vector of the form $$\displaystyle (x,y,z)\in\mathbb{R}^2$$?

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#### jayshizwiz

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...

#### dwsmith

MHF Hall of Honor
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)

Gotcha,
Thanks.