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Eliminate | A Wisdom Archive on Eliminate |  | Eliminate A selection of articles related to Eliminate |  |
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ARTICLES RELATED TO Eliminate | |
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 |  |  | Eliminate: Encyclopedia II - Gaussian elimination - ExampleSuppose you need to find numbers x, y, and z such that the following three equations are all simultaneously true:
2x + y − z = 8,
− 3x − y + 2z = − 11,
− 2x + y + 2z = − 3
This is called a system of linear equations for the unknowns x, y, and z. They are called linear bec ...
See also:Gaussian elimination, Gaussian elimination - History, Gaussian elimination - Numerical analysis, Gaussian elimination - Example, Gaussian elimination - Row echelon and reduced row echelon form, Gaussian elimination - Other applications, Gaussian elimination - Finding the inverse of a matrix, Gaussian elimination - The general algorithm to compute ranks and bases Read more here: » Gaussian elimination: Encyclopedia II - Gaussian elimination - Example |
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 |  |  | Eliminate: Encyclopedia II - Gaussian elimination - Numerical analysisThe computational complexity of Gaussian elimination is O(n3); that is, the number of operations required is (approximately) proportional to n3 if the matrix size is n × n.
This algorithm can be used on a computer for systems with thousands of equations and unknowns. It is, however, numerically unstable, at least on pathological examples; that is, floating-point errors committed throughout the computation are accumulated and may result in results far from the correct solution. For thi ...
See also:Gaussian elimination, Gaussian elimination - History, Gaussian elimination - Numerical analysis, Gaussian elimination - Example, Gaussian elimination - Row echelon and reduced row echelon form, Gaussian elimination - Other applications, Gaussian elimination - Finding the inverse of a matrix, Gaussian elimination - The general algorithm to compute ranks and bases Read more here: » Gaussian elimination: Encyclopedia II - Gaussian elimination - Numerical analysis |
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 |  |  | Eliminate: Encyclopedia II - Gaussian elimination - Row echelon and reduced row echelon formTwo special arrangements of matrix are called row echelon form and reduced row echelon form. The definitions of these terms depends on the first non-zero term in each row, called the row's leading coefficient. For a matrix to be in row echelon form (REF), each leading coefficient must equal 1. Furthermore the rows must be arranged as follows. As one moves from the top to the bottom of the matrix, the leading coefficients move from the left to the right and finally rows without any leading coefficient appear last. The final matrix in ...
See also:Gaussian elimination, Gaussian elimination - History, Gaussian elimination - Numerical analysis, Gaussian elimination - Example, Gaussian elimination - Row echelon and reduced row echelon form, Gaussian elimination - Other applications, Gaussian elimination - Finding the inverse of a matrix, Gaussian elimination - The general algorithm to compute ranks and bases Read more here: » Gaussian elimination: Encyclopedia II - Gaussian elimination - Row echelon and reduced row echelon form |
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 |  |  | Eliminate: Encyclopedia II - Tournament - Double-eliminationDouble-elimination tournaments are less cutthroat than single-elimination tournaments, as a player is allowed to lose one game without being dropped from the tournament. The winners of the first round move on to play each other in the "winners' bracket" in the second round; the losers of the first round move on to the "losers' bracket" and play each other in the second round. In each subsequent round, those players in the "losers' bracket" who lose a game are dropped from the tournament, whereas those who win get to advance to the next round ...
See also:Tournament, Tournament - Single-elimination, Tournament - Double-elimination, Tournament - Swiss style tournaments, Tournament - Brackets and initial matchups, Tournament - Byes, Tournament - Tiebreakers, Tournament - Poker, Tournament - Bridge Read more here: » Tournament: Encyclopedia II - Tournament - Double-elimination |
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