__Context__:

To show that

we need to prove we cannot shatter any set od

points. In this case we have

vectors of

, where

, hence we have

vector than the total number of dimensions (our space is

-dimensional). According to the theory of vector spaces when we have more vectors than dimensions of the space then they are linearly dependent (one of the vectors is a linear combination of the others). Which means that for instance our extra point

, can be computed by the equation (in

-dimensional space):

, (where not all

coefficients are zeros).

We need to show that we can't get

(

) dichotomies, where

is of

size.

__Problem:__
And now let me define my problem I have with understanding the video proof. Why do we correlate

coefficient with the

while they don't correlate? On what basis we can draw that

, and that's why

, hence we can't generate

?