Equivalent Systems and Equivalent Matrices

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Equivalent Systems and Equivalent Matrices
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Terminology

• A zero row is a row that consists entirely of
  zeros (all of its entries are 0)
• A nonzero row is a row with at least one nonzero
  entry.
• The first nonzero entry of a nonzero row is
  called its leading entry

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Row Echelon Matrices

• The matrix E is said to be in row echelon form
  if the following two conditions are satisfied
• Every zero row lies beneath every non zero row.
• The leading entry of a non zero row lies strictly
  to the right of the leading entry of any other
  preceding row.

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Row Echelon Matrices
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Reduced Row Echelon Form

• The matrix E is said to be in reduced row
  echelon form if the following two conditions are
  satisfied
• Every leading entry of E is 1.
• Each leading entry of E is the only nonzero
  element in its column.

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Modification

• For the sake of argument, let us introduce a
  modification in the previous system so that now
  looks like.

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