1.verifica-sottospazio.tex

\subsection{Verifica di sottospazio}
$S = \{ \vec{v} = (x_1, x_2, x_3) \in \mathbb{R}^3\ |\ x_1 + x_2 + x_3 = 0 \}$

$\vec{v} = (x_1, x_2, x_3) \qquad \vec{w} = (y_1, y_2, y_3)$

\begin{tabular}{l}
	$\vec{0} \in S \quad 0 + 0 + 0 = 0$ \\
	$\vec{v}+\vec{w} = (x_1+y_1, x_2+y_2, x_3+y_3)$ \\
	$\quad (x_1+y_1) + (x_2+y_2) + (x_3+y_3) = $ \\
	$\quad = (x_1 + x_2 + x_3) + (y_1+y_2+y_3) = 0$ \\
	$\lambda\vec{v} = (\lambda x_1, \lambda x_2, \lambda x_3)$ \\
	$\quad \lambda x_1 + \lambda x_2 + \lambda x_3 = \lambda(x_1+x_2+x_3) = 0$
\end{tabular}