# Prove that the set is not a subspace of vector space

• Mar 17th 2010, 04:29 PM
ephemeral1
Prove that the set is not a subspace of vector space
How can I verify that the following is not a subspace of the vector space with an example?

W is the set of all linear functions ax+b, where are is not equal to 0, in C(-infiniti, infiniti)
• Mar 17th 2010, 05:39 PM
Drexel28
Quote:

Originally Posted by ephemeral1
How can I verify that the following is not a subspace of the vector space with an example?

W is the set of all linear functions ax+b, where are is not equal to 0, in C(-infiniti, infiniti)

$\displaystyle -ax+b+ax+b=2b\notin \left\{mx+n:m,n\in\mathbb{R}-\{0\}\right\}$
• Mar 17th 2010, 05:52 PM
ephemeral1
Could you elaborate on your answer? I don't understand the last part of your answer. The one with R-{0}}. Thank you.
• Mar 17th 2010, 06:04 PM
Drexel28
Quote:

Originally Posted by ephemeral1
Could you elaborate on your answer? I don't understand the last part of your answer. The one with R-{0}}. Thank you.

If you take $\displaystyle x+1$ and $\displaystyle -x+1$ they are both in the set. But, $\displaystyle x+1+-x+1=2$ is not since it's leading coefficient is zero.