Determine if a set is a subspace of $\mathbb{C}^4$

Question

I have to determine if $$ W_1=\left\{(x^1, x^2, x^3, x^4)\in\mathbb{C}^4:\frac{x^1}{x^3}=2,\ x^2=2x^3\right\} $$ and $$ W_2=\left\{(x^1, x^2, x^3, x^4)\in\mathbb{C}^4:x^1-3x^2+2x^3=4\right\} $$ are subspaces of $\mathbb{C}^4$.

My attempt. I immediately conclude that $W_1$ and $W_2$ are not subspaces because $(0, 0, 0, 0)\notin W_1,W_2$. Indeed, in $W_1$, $x^3$ must be different from $0$ and, in $W_2$, $(x^1, x^2, x^3, x^4)=(0, 0, 0, 0)$ does not satisfy $x^1-2x^2+2x^3=4$. Is it right?

Thank You

Answer 1

You are right, fine arguments!