# Thread: dimension of a subspace

1. ## dimension of a subspace

A subspace W of R is defined by W={(x, 2y, 3z): x, y, z belongs to R }. How to find the dimension of W?

2. ## Re: dimension of a subspace

A subspace W of R is defined by W={(x, 2y, 3z): x, y, z belongs to R }. How to find the dimension of W?
What is $\displaystyle R~?$

3. ## Re: dimension of a subspace

Originally Posted by Plato
What is $\displaystyle R~?$
R is the set of real numbers.

4. ## Re: dimension of a subspace

R is the set of real numbers.
Then $\displaystyle W$ cannot be a subspace of $\displaystyle \mathbb{R}~!$

5. ## Re: dimension of a subspace

Sorry for the serious mistake in my post . The original question is
Show that W={(x, 2y, 3z): x, y, z belongs to R },where R is the set of real numbers, is a subspace. Find the dimension of W.

Well $\displaystyle \{(1,0,0),~(0,2,0),~{(0,0,3)\}\subset W$.