Prove that the given subset W is a subspace of
V , or show why it is not a subspace of V .

V = $$\mathbb{R}^\infty $$ is the subset of vectors (x1, x2, x3, ....) for which x3 = x2+x1, x4=x3+x2, .. in general xn+2 + xn+1 + xn for all
n$$\ge$$ 1

Question

Prove that the given subset W is a subspace of
V , or show why it is not a subspace of V . 

V = $$\mathbb{R}^\infty $$ is the subset of vectors (x1, x2, x3, ....) for which x3 = x2+x1, x4=x3+x2, .. in general xn+2 + xn+1 + xn for all 
n$$\ge$$ 1

turingtest · Answer

$$V=\mathbb R^{\infty}$$$$W=\left\{ \vec x_1,\vec x_2,\vec x_3,... \right\}:\vec x_{n+2}=\vec x_{n+1}+\vec x_n;n\ge1$$is $W$ a subspace of $V$ ?

turingtest · Answer

I just wanted to make the question more clear...

turingtest · Answer

don't you have a typo?
xn+2 + xn+1 + xn
?
should be 
xn+2 = xn+1 + xn
right?

anonymous · Answer

yes sorry that's what it should be!

anonymous · Answer

but i'm still not too sure of the answer or how to go about finding it.