Thread: 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

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: $\displaystyle U=\{t\cdot (a,b,c)\,\mid\,\,t\in\mathbb{R}\,,\,(a,b,c)\neq (0,0,0)\}$ 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

a,b,c are all real?