# Are B&W images of digits linear seperable

Given an image, expressed in the vector $\vec{v} = (v_1, \dots, v_n)\in \{0,1\}^n$

The vector $\vec{v}$ can represent images of the numbers 0 to 9. How do I know if this is linear seperable? Given the high dimension when we get big pictures, it becomes hard to reason about this, altough I think the answer is pretty straightforward.

What is a correct and (preferably) mathematical way of reasoning about this? I believe they are not linearly seperable, but I wouldn't know how to prove this.