# Thread: Prove that V is a subspace of Rn

1. ## Prove that V is a subspace of Rn

Let V = {x E Rn | Ax= λx} where A is an n x n matrix and λ is a real scalar, together with the usual operations for vector addition and scalar multiplication from Rn. Prove that V is a subspace of Rn.

2. ## Re: Prove that V is a subspace of Rn

you need to show that

$\forall x,y \in V,~a,b \in \mathbb{R},~a x + b y \in V$

3. ## Re: Prove that V is a subspace of Rn

Following on what romsek said, since A is a linear transformation, what is A(ax+ by)?