In Matt Thompson’s article “Matrilineal Patterns in the Book of Genesis” he discusses matrilineage in the Book of Genesis. Thompson recounts the story of Abraham, from when he was Abram (his name before his covenant with God) to the story of Jacob (Abraham’s grandson).
This story, in the Old Testament or the first book of the Torah, explains how Abraham and his wife Sarah’s descendants become the the chosen people. The chosen people are the Jews and they descended from not one of the many children Abraham had with his concubines but rather the one son he had with his wife Sarah, Isaac. From this union the Jewish people trace their descent. Because of the story of Abraham and his wife Sarah and not Abraham and the handmaiden Hager and their son Ishmael (who Muslims trace their descendents from including the prophet Muhammad) Jewish law states that in order to be considered Jewish in the classical sense your mother must be Jewish. The Jewish Religion is there for passed down through mothers, making it a matrilineage.
Although Judaism is traced in the matrilineage it is not a matriachy. This can be seen in Thompson’s article when he discusses the story of how Isaac found won his bride Rebekah. Isaac, or rather his servant, had to get Rebekah’s brother’s approval before he could take Rebekah back to Isaac’s village to become his wife. In that story and in many others in the Bible the male family members were the ones to make the decisions regardless of who was able to pass on the religion.