Echelon Form

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A rectangular matrix is in echelon form if

  1. If there are any, all zero rows are at the bottom
  2. The first non-zero entry (leading entry) of a row is to the right of any leading entries in the row above it
  3. All elements below a leading entry are zero For reduced row echelon form
  4. All leading entries, if any, are equal to 1.
  5. Leading entries are the only nonzero entry in their respective column.

Pivot

  • A Pivot in a matrix A is a location in A that corresponds to a leading 1 in the RREF of A
  • A Pivot column is the column of the pivot

Free Variable

Free variables are the variables of the non-pivot columns

  • Any choice of the free variables leads to a solution of the system
  • If you have any free variables you do not have a unique solution]

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