# Thread: Prove that T is a subspace in R^n

1. ## Prove that T is a subspace in R^n

T = { x E R^n | x . v = 0 for all v E S } ____________[E means 'element of']

"Let S be a subspace of of R^n and let that is, T is the set of all vectors in R^n that are orthogonal to every vector in S."

thanks again

2. ## Re: Prove that T is a subspace in R^n

You just have to show that all the axioms hold for all vectors in T

Vector space - Wikipedia, the free encyclopedia

3. ## Re: Prove that T is a subspace in R^n

Originally Posted by Brennox
According to a well known theorem you have to prove: (i) $0\in T$. (ii) For all $x,y\in T$, $x+y\in T$. (iii) For all $\lambda\in\mathbb{R}$ and for all $x\in T$, $\lambda x\in T.$ Try to prove those properties.