Real Linear Subspace Contains Zero Vector

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.

$\blacksquare$

Also see

• Zero Subspace is Subspace