My Rage Against the Machine.

First Establishing Who is a Jew:
The Mishnah (Kiddushin 3:12) states that, to be a Jew, one must be either the child of a Jewish mother or a convert to Judaism.

So To be Jewish your Mother Has to Be Jewish(From The Tribes of Judah, Levi, Benjamin)

Which Tribes are Jewish?:
Brief History Lesson - 13 Tribes of Israel & The Split

After King Solomon died the 13 tribes of Israel split into The North Kingdom of Israel & The South Kingdom of Judah.
The Tribes Living in The North Kingdom of Israel
-Asher
-Dan
-Gad
-Issachar
-Joesph
-Naptali
-Reuben
-Simeon
-Zebulun
-Ephraim and Manasseh

The Tribes Living in the South Kingdom of Judah
-Judah
-Levi
-Benjamin

So from this we can counclude several things.

The Southern Kingdom of Judah:
First, Judah is Jewish.
Second, Levi had already established a covenant with God and was Jewish(Exodous 32: 26-29)
Third, Benjamin sided with Judah and lived in Judah.

Judah is Jewish.
Levi is Jewish
Benjamin decided to live with Judah and Levi, who where entirely Jewish. I think that they may have converted to Judaism.

The North Kingdom of Israel:

Ten Tribes Decided to create The North Kingdom of Israel.
They were conquered by The Assyrians and Deported. They became the Ten Lost Tribes of Israel