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

1. ## 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)

2. 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)
$-ax+b+ax+b=2b\notin \left\{mx+n:m,n\in\mathbb{R}-\{0\}\right\}$

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