Hi all,

Here's a question I'm struggling with:

Show that the set of all elements of R^2 of the form (a, -a), where a is any real number, is a subspace of R^2. Give a geometric interpretation of the subspace. Any suggestions?

Thanks,

Jim

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- May 13th 2008, 12:11 PMJim NewtVector subspace question
Hi all,

Here's a question I'm struggling with:

Show that the set of all elements of R^2 of the form (a, -a), where a is any real number, is a subspace of R^2. Give a geometric interpretation of the subspace. Any suggestions?

Thanks,

Jim - May 13th 2008, 12:20 PMPlato
1) Does the set contain (0,0)?

2) Is the set closed under vector addition?

3) Is the set closed with respect to scalar multiplication? - May 13th 2008, 12:23 PMJim Newt
- May 13th 2008, 01:23 PMTheEmptySet