Which are subspaces of r3

No packages or subscriptions, pay only for the time you need. Add comment. The correct answers are a and c. My reasoning is as follows. Any subspace of R 3 must contain the same zero vector and have the same vector operations as R 3 vector addition and scalar multiplication. Notice that b and d do NOT contain the zero vector 0,0,0 , so could not possibly be subspaces of this vector space. As for a , it is a two-dimensional plane passing through the origin the xy-plane , so is a subspace.

I have attached an image of the question I am having trouble with. Is a subspace since it is the set of solutions to a homogeneous linear equation. Is a subspace. I know that to be a subspace, it must be closed under scalar multiplication and vector addition, but there was no equation linking the variables, so I just jumped into thinking it would be a subspace So, not a subspace. Again, I was not sure how to check if it is closed under vector addition and multiplication.

A similar definition holds for problem 5. Hence it is a subspace. Sign up to join this community. The best answers are voted up and rise to the top. Stack Overflow for Teams — Collaborate and share knowledge with a private group.

Create a free Team What is Teams? Learn more. Finding which sets are subspaces of R3 Ask Question. Asked 3 years, 3 months ago. Active 12 months ago. Viewed 17k times. I appreciate any help. Thank you. Michel Michel 1 1 gold badge 3 3 silver badges 10 10 bronze badges.