Thread: Subspace for R^3

{(x1, x2, x3)^T | x3 = x1 or x3 = x2}

I know it is not a subspace of R^3, however I'm not exactly sure why. I'm thinking it is because of the OR in the statement? In an earlier problem I had to prove that the same set and statement x1 = x2 = x3 is a subspace, which held true. But this OR is throwing me off. Any ideas?

Originally Posted by pakman

{(x1, x2, x3)^T | x3 = x1 or x3 = x2}

I know it is not a subspace of R^3, however I'm not exactly sure why. I'm thinking it is because of the OR in the statement? In an earlier problem I had to prove that the same set and statement x1 = x2 = x3 is a subspace, which held true. But this OR is throwing me off. Any ideas?

This is not a subspace it is not closed

Example

consider

both fit the above criteria but



This is not in the "subspace" because

but both