one-dimensional subspace of R^3

**charikaar** · Nov 18th 2009, 10:43 AM

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

**tonio** · Nov 18th 2009, 10:47 AM

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

**charikaar** · Nov 18th 2009, 12:09 PM

a,b,c are all real?

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