# one-dimensional subspace of R^3

• November 18th 2009, 10:43 AM
charikaar
one-dimensional subspace of R^3
Question:Give an example of a 1-dimensional subspace U of R3.

Answer: Any line through the origin is a one-dimensional subspace of R3.

How do i write this as a set? i mean U=?

thanks
• November 18th 2009, 10:47 AM
tonio
Quote:

Originally Posted by charikaar
Question:Give an example of a 1-dimensional subspace U of R3.

Answer: Any line through the origin is a one-dimensional subspace of R3.

How do i write this as a set? i mean U=?

thanks

You should know this from analytic geometry: $U=\{t\cdot (a,b,c)\,\mid\,\,t\in\mathbb{R}\,,\,(a,b,c)\neq (0,0,0)\}$ is a straight line through the origin in 3-dimensional space, which is EXACTLY the same as the span of one non-zero vector...

Tonio
• November 18th 2009, 12:09 PM
charikaar
a,b,c are all real?