Real Linear Subspace Contains Zero Vector
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Theorem
Let $\mathbb W \subseteq \R^n$ such that $\mathbb W$ is a linear subspace of $\R^n$.
Then $\mathbb W$ contains the zero vector:
- $\mathbf 0_{n \times 1} = \begin{bmatrix}
0 \\ 0 \\ \vdots \\ 0 \end{bmatrix} \in \mathbb W$
Proof
This is a consequence of Vector Subspace of Real Vector Space.
$\blacksquare$