What are the subspaces of ℝ, ℝ^2, and ℝ^3?

[mtayab1994]

Homework Statement

Find all subspaces of the vector spaces: (ℝ+,.) , (ℝ^2 +,.) , (ℝ^3 +,.)

The Attempt at a Solution

For ℝ the only subspace i can think of is {0}

For ℝ^2 if found {0} R^2 itself and any set of the form L=cu for u≠0.

For ℝ^3 if found those of R^2 plus R^3 . Are they correct?

 

[voko]

For the second case, you found that L = cu, where c is some given constant, including 0, defines a subspace. Find a similar equation for the next case, and think how you can generalize that.