'Matrilineality in Judaism is the view that people born of a Jewish mother are themselves Jewish. The Torah does not explicitly discuss the conferring of Jewish status through matrilineality, and in apparent contrast to this position, the Tanakh (Hebrew Bible) provides many examples of Israelite men whose children by foreign women appear to have been accepted as Israelite. However, Jewish oral tradition codified in Mishnah by the 2nd century CE maintains that matrilineality was always the rule, and adduces indirect textual evidence from the Torah, with the implicit assumption that the women in question converted to Judaism.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, (ger tzedek, "righteous convert")'
http://en.wikipedia.org/wiki/Matrilineality_in_Judaism
Thats obviously false. Why?
According to Professor Shaye Cohen of Brown University:
"Numerous Israelites heroes and kings married foreign women: for example, Judah married a Canaanite, Joseph an Egyptian, Moses a Midianite and an Ethiopian, David a Philistine, and Solomon women of every description. By her marriage with an Israelite man a foreign women joined the clan, people, and religion of her husband. It never occurred to anyone in pre-exilic times to argue that such marriages were null and void, that foreign women must "convert" to Judaism, or that the off-spring of the marriage were not Israelite if the women did not convert."
So either the Israelites were not followers of Judaism or there has been a change in the thought of what constitutes a Jew
Tracing to when matrilineal descent became part of Judaism:
Sometime during the Roman occupation and the Second Temple period, a law of matrilineal descent, which defined a Jew as someone with a Jewish mother, was adopted. By the 2nd century CE, it was clearly practiced.
http://judaism.about.com/od/whoisajew/a/whoisjewdescent.htm