## 每週問題 October 22, 2012

Let $\mathcal{V}$ be the solution space of

$x_1 + x_2 +\cdots + x_n = 0$

and $\mathcal{W}$ be the solution space of

$x_1 = x_2 = \cdots = x_n$,

where $x_i \in\mathbb{R}$, $i = 1, \ldots, n$. Show that $\mathcal{V}\oplus\mathcal{W}=\mathbb{R}^n$.

PowSol-Oct-22-12