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Each step in Gaussian elimination or Gauss–Jordan elimination consists of making one of the entries aij of the matrix equal to 1 and using this to produce zeros elsewhere in the j-th column. This process is known as a pivot operation, with aij as pivot. The pivot, of course, must be non-zero. This corresponds to solving one of the equations for one of the unknowns xj and substituting this into the other equations.

Subjects: Mathematics.

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