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Numerical Linear Algebra with Applications by William Ford

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Example 11.11

Let A=[ 1101111011112010]si134_e. This example illustrates the process just described that derives GEPP.

Start: L=[ 1000010000100001],P=[ 1000010000100001]si135_e i = 1: Exchange rows 1 and 4. Eliminate entries at indices (2, 1) − (4, 1):

E1=E41(12)E31(12)E21(12)=[ 1000010000100.5001][ 100001000.50100001][ 10000.510000100001]=[ 10000.51000.50100.5001]P1=[ 0001010000101000]E1P1A=[ 2010011.50010.51010.51]

si136_e

i = 2: A row exchange is not ...

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