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Gauss-Jordan Elimination
A method of solving a linear system of equations. This is done by transforming the system's augmented matrix into reduced row-echelon form by means of row operations.

Gaussian Elimination
A method of solving a linear system of equations. This is done by transforming the system's augmented matrix into row-echelon form by means of row operations. Then the system is solved by back-substitution.  

Palestine: History
Introduction
Palestine stands alone among the Roman provinces in that here only there existed a national identity strong enough effectively to challenge Roman rule.  That identity depended on a body of Hebrew religious writings that constituted a concrete locus for the formation of durable political and religious institutions.  This locus and these institutions provided the framework for the two great rebellions that the Romans faced in Palestine in the first and second centuries CE; the messianic promise that the writings contained and misgovernment and Romanizing policy provided the motivations for revolt. Precisely because these rebellions grew out out of the Jewish national identity, the Romans found them far more dangerous than any revolt based on generalized resistance to Romanization, Hellenization, or paganism or on any particular program for a new political and religious order--and many such programs did indeed emerge from this remarkable region.  The section on People and Places offers further information on the Jewish people and their religious writings.  Here I offer a survey of the history of the region with particular reference to the problem nationalism presented to the Roman rulers, at least until the Romans demolished the institutions (but not the writings and the national identity) in the 130s.  Jewish resistance to Roman rule explains why the process of Romanization in Palestine had to involve not only the founding of colonies and other Greco-Roman cities and the co-optation of the local elites but also forced migration--what we now call ethnic cleansing--and the permanent stationing of an unusually large legionary force.  After the 130s Palestine lost much of its unusual and problematic features with respect to its position in the imperial system, and the large legionary force moved elsewhere.  Still, the religious identity now of the Samaritans continued to challenge the authority of the government until the end of Late Antiquity.

To 6 CE: From Client Kingdom to Province
The Roman senate awarded Herod the kingdom of Judaea in 40 BCE but left him to master it largely with his own resources.  Subsequently Antony detached the coastal part of the kingdom and gave it to Cleopatra, but this arrangement lasted only until the defeat of Antony and Cleopatra at Actium in 31 BCE.  After Actium, Herod, who had backed Antony, hastened to Rhodes to meet the victorious Octavian, who confirmed him in his place and soon awarded him additional territory.  The map (like the others on this page, based on the IAM map, here with additional information from King Herod's Dream) shows Herod's realm at its greatest extent.  Herod's rule lasted until until his death in 4 BCE.   He was responsible for the initial phases of Romanization because of his widespread patronage of Greco-Roman culture and his foundation of cities in the Greek style at Caesarea and Sebaste.  In addition, ever since the Romans arrived in the 60s they had liberated Greek cities from Hasmonean rule, especially on the coast and in the Decapolis; this policy continued after the death of Herod. In the period between Pompey's arrival and initial political settlements in the sixties and the death of Herod, Rome made its influence felt in the Eastern Mediterranean primarily through the presence of--probably--three legions in Syria.  This entire force in addition to Syrian auxiliaries came to Judaea after Herod died in order to suppress a popular revolt against the Herodians.  Meanwhile Herod's heir Archelaus went to...
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