# 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

Originally Posted by Suvadip
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 $R~?$

3. ## Re: dimension of a subspace

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

4. ## Re: dimension of a subspace

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

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.

I know the solution of the first part. Please help me for the second part.

6. ## Re: dimension of a subspace

Originally Posted by Suvadip
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.
I know the solution of the first part. Please help me for the second part.
Well $\{(1,0,0),~(0,2,0),~{(0,0,3)\}\subset W$.