Program to handle the Arithmetic in the Row Reduction of a Linear System
VisualBASIC version (c)1999, Glyn George.
Linear System:
a b d e g h Number
Row 1: 0/1 0/1 -1/1 0/1 4/1 -1/1 73/4 [Equation (1)]
Row 2: 0/1 0/1 0/1 -1/1 -2/1 4/1 25/1 [Equation (2)]
Row 3: -1/1 0/1 4/1 -1/1 -1/1 0/1 0/1 [Equation (4)]
Row 4: 0/1 -1/1 -2/1 4/1 0/1 -1/1 0/1 [Equation (5)]
Row 5: 4/1 -1/1 -1/1 0/1 0/1 0/1 20/1 [Equation (7)]
Row 6: -2/1 4/1 0/1 -1/1 0/1 0/1 10/1 [Equation (8)]
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Selected row operation: Swap rows 1 and 3 .
Linear System:
Row 1: -1/1 0/1 4/1 -1/1 -1/1 0/1 0/1
Row 2: 0/1 0/1 0/1 -1/1 -2/1 4/1 25/1
Row 3: 0/1 0/1 -1/1 0/1 4/1 -1/1 73/4
Row 4: 0/1 -1/1 -2/1 4/1 0/1 -1/1 0/1
Row 5: 4/1 -1/1 -1/1 0/1 0/1 0/1 20/1
Row 6: -2/1 4/1 0/1 -1/1 0/1 0/1 10/1
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Selected row operation: Divide row 1 by -1 / 1 .
Linear System:
Row 1: 1/1 0/1 -4/1 1/1 1/1 0/1 0/1
Row 2: 0/1 0/1 0/1 -1/1 -2/1 4/1 25/1
Row 3: 0/1 0/1 -1/1 0/1 4/1 -1/1 73/4
Row 4: 0/1 -1/1 -2/1 4/1 0/1 -1/1 0/1
Row 5: 4/1 -1/1 -1/1 0/1 0/1 0/1 20/1
Row 6: -2/1 4/1 0/1 -1/1 0/1 0/1 10/1
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Selected row operation: Subtract 4 / 1 times row 1 from row 5 .
Linear System:
Row 1: 1/1 0/1 -4/1 1/1 1/1 0/1 0/1
Row 2: 0/1 0/1 0/1 -1/1 -2/1 4/1 25/1
Row 3: 0/1 0/1 -1/1 0/1 4/1 -1/1 73/4
Row 4: 0/1 -1/1 -2/1 4/1 0/1 -1/1 0/1
Row 5: 0/1 -1/1 15/1 -4/1 -4/1 0/1 20/1
Row 6: -2/1 4/1 0/1 -1/1 0/1 0/1 10/1
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Selected row operation: Subtract -2 / 1 times row 1 from row 6 .
Linear System:
Row 1: 1/1 0/1 -4/1 1/1 1/1 0/1 0/1
Row 2: 0/1 0/1 0/1 -1/1 -2/1 4/1 25/1
Row 3: 0/1 0/1 -1/1 0/1 4/1 -1/1 73/4
Row 4: 0/1 -1/1 -2/1 4/1 0/1 -1/1 0/1
Row 5: 0/1 -1/1 15/1 -4/1 -4/1 0/1 20/1
Row 6: 0/1 4/1 -8/1 1/1 2/1 0/1 10/1
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Selected row operation: Swap rows 4 and 2 .
Linear System:
Row 1: 1/1 0/1 -4/1 1/1 1/1 0/1 0/1
Row 2: 0/1 -1/1 -2/1 4/1 0/1 -1/1 0/1
Row 3: 0/1 0/1 -1/1 0/1 4/1 -1/1 73/4
Row 4: 0/1 0/1 0/1 -1/1 -2/1 4/1 25/1
Row 5: 0/1 -1/1 15/1 -4/1 -4/1 0/1 20/1
Row 6: 0/1 4/1 -8/1 1/1 2/1 0/1 10/1
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Selected row operation: Divide row 2 by -1 / 1 .
Linear System:
Row 1: 1/1 0/1 -4/1 1/1 1/1 0/1 0/1
Row 2: 0/1 1/1 2/1 -4/1 0/1 1/1 0/1
Row 3: 0/1 0/1 -1/1 0/1 4/1 -1/1 73/4
Row 4: 0/1 0/1 0/1 -1/1 -2/1 4/1 25/1
Row 5: 0/1 -1/1 15/1 -4/1 -4/1 0/1 20/1
Row 6: 0/1 4/1 -8/1 1/1 2/1 0/1 10/1
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Selected row operation: Subtract -1 / 1 times row 2 from row 5 .
Linear System:
Row 1: 1/1 0/1 -4/1 1/1 1/1 0/1 0/1
Row 2: 0/1 1/1 2/1 -4/1 0/1 1/1 0/1
Row 3: 0/1 0/1 -1/1 0/1 4/1 -1/1 73/4
Row 4: 0/1 0/1 0/1 -1/1 -2/1 4/1 25/1
Row 5: 0/1 0/1 17/1 -8/1 -4/1 1/1 20/1
Row 6: 0/1 4/1 -8/1 1/1 2/1 0/1 10/1
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Selected row operation: Subtract 4 / 1 times row 2 from row 6 .
Linear System:
Row 1: 1/1 0/1 -4/1 1/1 1/1 0/1 0/1
Row 2: 0/1 1/1 2/1 -4/1 0/1 1/1 0/1
Row 3: 0/1 0/1 -1/1 0/1 4/1 -1/1 73/4
Row 4: 0/1 0/1 0/1 -1/1 -2/1 4/1 25/1
Row 5: 0/1 0/1 17/1 -8/1 -4/1 1/1 20/1
Row 6: 0/1 0/1 -16/1 17/1 2/1 -4/1 10/1
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Selected row operation: Divide row 3 by -1 / 1 .
Linear System:
Row 1: 1/1 0/1 -4/1 1/1 1/1 0/1 0/1
Row 2: 0/1 1/1 2/1 -4/1 0/1 1/1 0/1
Row 3: 0/1 0/1 1/1 0/1 -4/1 1/1 -73/4
Row 4: 0/1 0/1 0/1 -1/1 -2/1 4/1 25/1
Row 5: 0/1 0/1 17/1 -8/1 -4/1 1/1 20/1
Row 6: 0/1 0/1 -16/1 17/1 2/1 -4/1 10/1
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Selected row operation: Subtract 17 / 1 times row 3 from row 5 .
Linear System:
Row 1: 1/1 0/1 -4/1 1/1 1/1 0/1 0/1
Row 2: 0/1 1/1 2/1 -4/1 0/1 1/1 0/1
Row 3: 0/1 0/1 1/1 0/1 -4/1 1/1 -73/4
Row 4: 0/1 0/1 0/1 -1/1 -2/1 4/1 25/1
Row 5: 0/1 0/1 0/1 -8/1 64/1 -16/1 1321/4
Row 6: 0/1 0/1 -16/1 17/1 2/1 -4/1 10/1
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Selected row operation: Subtract -16 / 1 times row 3 from row 6 .
Linear System:
Row 1: 1/1 0/1 -4/1 1/1 1/1 0/1 0/1
Row 2: 0/1 1/1 2/1 -4/1 0/1 1/1 0/1
Row 3: 0/1 0/1 1/1 0/1 -4/1 1/1 -73/4
Row 4: 0/1 0/1 0/1 -1/1 -2/1 4/1 25/1
Row 5: 0/1 0/1 0/1 -8/1 64/1 -16/1 1321/4
Row 6: 0/1 0/1 0/1 17/1 -62/1 12/1 -282/1
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Selected row operation: Divide row 4 by -1 / 1 .
Linear System:
Row 1: 1/1 0/1 -4/1 1/1 1/1 0/1 0/1
Row 2: 0/1 1/1 2/1 -4/1 0/1 1/1 0/1
Row 3: 0/1 0/1 1/1 0/1 -4/1 1/1 -73/4
Row 4: 0/1 0/1 0/1 1/1 2/1 -4/1 -25/1
Row 5: 0/1 0/1 0/1 -8/1 64/1 -16/1 1321/4
Row 6: 0/1 0/1 0/1 17/1 -62/1 12/1 -282/1
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Selected row operation: Subtract -8 / 1 times row 4 from row 5 .
Linear System:
Row 1: 1/1 0/1 -4/1 1/1 1/1 0/1 0/1
Row 2: 0/1 1/1 2/1 -4/1 0/1 1/1 0/1
Row 3: 0/1 0/1 1/1 0/1 -4/1 1/1 -73/4
Row 4: 0/1 0/1 0/1 1/1 2/1 -4/1 -25/1
Row 5: 0/1 0/1 0/1 0/1 80/1 -48/1 521/4
Row 6: 0/1 0/1 0/1 17/1 -62/1 12/1 -282/1
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Selected row operation: Subtract 17 / 1 times row 4 from row 6 .
Linear System:
Row 1: 1/1 0/1 -4/1 1/1 1/1 0/1 0/1
Row 2: 0/1 1/1 2/1 -4/1 0/1 1/1 0/1
Row 3: 0/1 0/1 1/1 0/1 -4/1 1/1 -73/4
Row 4: 0/1 0/1 0/1 1/1 2/1 -4/1 -25/1
Row 5: 0/1 0/1 0/1 0/1 80/1 -48/1 521/4
Row 6: 0/1 0/1 0/1 0/1 -96/1 80/1 143/1
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Selected row operation: Divide row 5 by 80 / 1 .
Linear System:
Row 1: 1/1 0/1 -4/1 1/1 1/1 0/1 0/1
Row 2: 0/1 1/1 2/1 -4/1 0/1 1/1 0/1
Row 3: 0/1 0/1 1/1 0/1 -4/1 1/1 -73/4
Row 4: 0/1 0/1 0/1 1/1 2/1 -4/1 -25/1
Row 5: 0/1 0/1 0/1 0/1 1/1 -3/5 521/320
Row 6: 0/1 0/1 0/1 0/1 -96/1 80/1 143/1
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Selected row operation: Subtract -96 / 1 times row 5 from row 6 .
Linear System:
Row 1: 1/1 0/1 -4/1 1/1 1/1 0/1 0/1
Row 2: 0/1 1/1 2/1 -4/1 0/1 1/1 0/1
Row 3: 0/1 0/1 1/1 0/1 -4/1 1/1 -73/4
Row 4: 0/1 0/1 0/1 1/1 2/1 -4/1 -25/1
Row 5: 0/1 0/1 0/1 0/1 1/1 -3/5 521/320
Row 6: 0/1 0/1 0/1 0/1 0/1 112/5 2993/10
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Selected row operation: Divide row 6 by 112 / 5 .
Linear System:
Row 1: 1/1 0/1 -4/1 1/1 1/1 0/1 0/1
Row 2: 0/1 1/1 2/1 -4/1 0/1 1/1 0/1
Row 3: 0/1 0/1 1/1 0/1 -4/1 1/1 -73/4
Row 4: 0/1 0/1 0/1 1/1 2/1 -4/1 -25/1
Row 5: 0/1 0/1 0/1 0/1 1/1 -3/5 521/320
Row 6: 0/1 0/1 0/1 0/1 0/1 1/1 2993/224
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Note that back substitution could be used from this echelon form.
----------------------------------------------------------------------------- Selected row operation: Subtract -4 / 1 times row 3 from row 1 . Linear System: Row 1: 1/1 0/1 0/1 1/1 -15/1 4/1 -73/1 Row 2: 0/1 1/1 2/1 -4/1 0/1 1/1 0/1 Row 3: 0/1 0/1 1/1 0/1 -4/1 1/1 -73/4 Row 4: 0/1 0/1 0/1 1/1 2/1 -4/1 -25/1 Row 5: 0/1 0/1 0/1 0/1 1/1 -3/5 521/320 Row 6: 0/1 0/1 0/1 0/1 0/1 1/1 2993/224 ----------------------------------------------------------------------------- Selected row operation: Subtract 2 / 1 times row 3 from row 2 . Linear System: Row 1: 1/1 0/1 0/1 1/1 -15/1 4/1 -73/1 Row 2: 0/1 1/1 0/1 -4/1 8/1 -1/1 73/2 Row 3: 0/1 0/1 1/1 0/1 -4/1 1/1 -73/4 Row 4: 0/1 0/1 0/1 1/1 2/1 -4/1 -25/1 Row 5: 0/1 0/1 0/1 0/1 1/1 -3/5 521/320 Row 6: 0/1 0/1 0/1 0/1 0/1 1/1 2993/224 ----------------------------------------------------------------------------- Selected row operation: Subtract 1 / 1 times row 4 from row 1 . Linear System: Row 1: 1/1 0/1 0/1 0/1 -17/1 8/1 -48/1 Row 2: 0/1 1/1 0/1 -4/1 8/1 -1/1 73/2 Row 3: 0/1 0/1 1/1 0/1 -4/1 1/1 -73/4 Row 4: 0/1 0/1 0/1 1/1 2/1 -4/1 -25/1 Row 5: 0/1 0/1 0/1 0/1 1/1 -3/5 521/320 Row 6: 0/1 0/1 0/1 0/1 0/1 1/1 2993/224 ----------------------------------------------------------------------------- Selected row operation: Subtract -4 / 1 times row 4 from row 2 . Linear System: Row 1: 1/1 0/1 0/1 0/1 -17/1 8/1 -48/1 Row 2: 0/1 1/1 0/1 0/1 16/1 -17/1 -127/2 Row 3: 0/1 0/1 1/1 0/1 -4/1 1/1 -73/4 Row 4: 0/1 0/1 0/1 1/1 2/1 -4/1 -25/1 Row 5: 0/1 0/1 0/1 0/1 1/1 -3/5 521/320 Row 6: 0/1 0/1 0/1 0/1 0/1 1/1 2993/224 ----------------------------------------------------------------------------- Selected row operation: Subtract -17 / 1 times row 5 from row 1 . Linear System: Row 1: 1/1 0/1 0/1 0/1 0/1 -11/5 -6503/320 Row 2: 0/1 1/1 0/1 0/1 16/1 -17/1 -127/2 Row 3: 0/1 0/1 1/1 0/1 -4/1 1/1 -73/4 Row 4: 0/1 0/1 0/1 1/1 2/1 -4/1 -25/1 Row 5: 0/1 0/1 0/1 0/1 1/1 -3/5 521/320 Row 6: 0/1 0/1 0/1 0/1 0/1 1/1 2993/224 ----------------------------------------------------------------------------- Selected row operation: Subtract 16 / 1 times row 5 from row 2 . Linear System: Row 1: 1/1 0/1 0/1 0/1 0/1 -11/5 -6503/320 Row 2: 0/1 1/1 0/1 0/1 0/1 -37/5 -1791/20 Row 3: 0/1 0/1 1/1 0/1 -4/1 1/1 -73/4 Row 4: 0/1 0/1 0/1 1/1 2/1 -4/1 -25/1 Row 5: 0/1 0/1 0/1 0/1 1/1 -3/5 521/320 Row 6: 0/1 0/1 0/1 0/1 0/1 1/1 2993/224 ----------------------------------------------------------------------------- Selected row operation: Subtract -4 / 1 times row 5 from row 3 . Linear System: Row 1: 1/1 0/1 0/1 0/1 0/1 -11/5 -6503/320 Row 2: 0/1 1/1 0/1 0/1 0/1 -37/5 -1791/20 Row 3: 0/1 0/1 1/1 0/1 0/1 -7/5 -939/80 Row 4: 0/1 0/1 0/1 1/1 2/1 -4/1 -25/1 Row 5: 0/1 0/1 0/1 0/1 1/1 -3/5 521/320 Row 6: 0/1 0/1 0/1 0/1 0/1 1/1 2993/224 ----------------------------------------------------------------------------- Selected row operation: Subtract 2 / 1 times row 5 from row 4 . Linear System: Row 1: 1/1 0/1 0/1 0/1 0/1 -11/5 -6503/320 Row 2: 0/1 1/1 0/1 0/1 0/1 -37/5 -1791/20 Row 3: 0/1 0/1 1/1 0/1 0/1 -7/5 -939/80 Row 4: 0/1 0/1 0/1 1/1 0/1 -14/5 -4521/160 Row 5: 0/1 0/1 0/1 0/1 1/1 -3/5 521/320 Row 6: 0/1 0/1 0/1 0/1 0/1 1/1 2993/224 ----------------------------------------------------------------------------- Selected row operation: Subtract -11 / 5 times row 6 from row 1 . Linear System: Row 1: 1/1 0/1 0/1 0/1 0/1 0/1 4065/448 Row 2: 0/1 1/1 0/1 0/1 0/1 -37/5 -1791/20 Row 3: 0/1 0/1 1/1 0/1 0/1 -7/5 -939/80 Row 4: 0/1 0/1 0/1 1/1 0/1 -14/5 -4521/160 Row 5: 0/1 0/1 0/1 0/1 1/1 -3/5 521/320 Row 6: 0/1 0/1 0/1 0/1 0/1 1/1 2993/224 ----------------------------------------------------------------------------- Selected row operation: Subtract -37 / 5 times row 6 from row 2 . Linear System: Row 1: 1/1 0/1 0/1 0/1 0/1 0/1 4065/448 Row 2: 0/1 1/1 0/1 0/1 0/1 0/1 2089/224 Row 3: 0/1 0/1 1/1 0/1 0/1 -7/5 -939/80 Row 4: 0/1 0/1 0/1 1/1 0/1 -14/5 -4521/160 Row 5: 0/1 0/1 0/1 0/1 1/1 -3/5 521/320 Row 6: 0/1 0/1 0/1 0/1 0/1 1/1 2993/224 ----------------------------------------------------------------------------- Selected row operation: Subtract -7 / 5 times row 6 from row 3 . Linear System: Row 1: 1/1 0/1 0/1 0/1 0/1 0/1 4065/448 Row 2: 0/1 1/1 0/1 0/1 0/1 0/1 2089/224 Row 3: 0/1 0/1 1/1 0/1 0/1 0/1 223/32 Row 4: 0/1 0/1 0/1 1/1 0/1 -14/5 -4521/160 Row 5: 0/1 0/1 0/1 0/1 1/1 -3/5 521/320 Row 6: 0/1 0/1 0/1 0/1 0/1 1/1 2993/224 ----------------------------------------------------------------------------- Selected row operation: Subtract -14 / 5 times row 6 from row 4 . Linear System: Row 1: 1/1 0/1 0/1 0/1 0/1 0/1 4065/448 Row 2: 0/1 1/1 0/1 0/1 0/1 0/1 2089/224 Row 3: 0/1 0/1 1/1 0/1 0/1 0/1 223/32 Row 4: 0/1 0/1 0/1 1/1 0/1 0/1 293/32 Row 5: 0/1 0/1 0/1 0/1 1/1 -3/5 521/320 Row 6: 0/1 0/1 0/1 0/1 0/1 1/1 2993/224 ----------------------------------------------------------------------------- Selected row operation: Subtract -3 / 5 times row 6 from row 5 . Linear System: Row 1: 1/1 0/1 0/1 0/1 0/1 0/1 4065/448 Row 2: 0/1 1/1 0/1 0/1 0/1 0/1 2089/224 Row 3: 0/1 0/1 1/1 0/1 0/1 0/1 223/32 Row 4: 0/1 0/1 0/1 1/1 0/1 0/1 293/32 Row 5: 0/1 0/1 0/1 0/1 1/1 0/1 4321/448 Row 6: 0/1 0/1 0/1 0/1 0/1 1/1 2993/224 ----------------------------------------------------------------------------- Program execution terminated.
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