Why do we need to drop one dummy variable?

For an example if in our data set there is a variable like location like:

Location ----------CaliforniaNew YorkFlorida

We have to convert them like

1  0  00  1  00  0  1

But it was suggested we have to discard one dummy variable, no matter how many dummy variables are there .

Reason:

Because the third dummy can be explained as the linear combination of the first two:

FL = 1 - (CA + NY)

if you have n variable then:

nth = 1 - (sum of all other)