This matrix is not reduced for two reasons:

• The leading entry in Row 1 does not have its column cleared:

  	0	1	0	0
  	1	0	1/3	1/3
  	0	1	0	0

• The leading entry in Row 1 is not to the left of the leading entry in Row 2.

To remedy the first problem, pivot on the leading entry in Row 1 to clear its column:

0 1 0 0 1 0 1/3 1/3 0 1 0 0 R3-R1

0 1 0 0 1 0 1/3 1/3 0 0 0 0

To remedy the second problem, switch Rows 1 and 2, to get

	1	0	1/3	1/3
	0	1	0	0
	0	0	0	0

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