|1.||a short shaft or pin supporting something that turns; fulcrum|
|2.||the end of a shaft or arbor that terminates in a bearing|
|3.||a person or thing upon which progress, success, etc, depends|
|4.||the person or position from which a military formation takes its reference, as when altering position|
|5.||(tr) to mount on or provide with a pivot or pivots|
|6.||(intr) to turn on or as if on a pivot|
|[C17: from Old French; perhaps related to Old Provençal pua tooth of a comb]|
in linear and multilinear algebra, a process for finding the solutions of a system of simultaneous linear equations by first solving one of the equations for one variable (in terms of all the others) and then substituting this expression into the remaining equations. The result is a new system in which the number of equations and variables is one less than in the original system. The same procedure is applied to another variable and the process of reduction continued until there remains one equation, in which the only unknown quantity is the last variable. Solving this equation makes it possible to "back substitute" this value in an earlier equation that contains this variable and one other unknown in order to solve for another variable. This process is continued until all the original variables have been evaluated. The whole process is greatly simplified using matrix operations, which can be performed by computers.
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