Algebra lineare Esempi

Problemi più comuni
Algebra lineare
Trovare il Rango [[1,0,0,1,1,0,0,0,0,0],[1,1,1,0,0,0,0,0,0,0],[0,1,0,1,0,0,0,0,0,0],[0,1,0,2,1,0,0,0,0,0],[1,1,0,0,0,0,0,0,0,0],[0,0,1,0,1,0,0,0,0,0],[0,0,1,0,0,0,0,0,0,1],[0,0,0,0,0,1,0,0,0,0],[0,0,0,0,0,1,1,1,1,0],[0,0,0,0,0,0,1,1,0,0]]
[1001100000111000000001010000000102100000110000000000101000000010000001000001000000000111100000001100]⎡⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢⎣1001100000111000000001010000000102100000110000000000101000000010000001000001000000000111100000001100⎤⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥⎦
Passaggio 1
Trova la forma ridotta a scala per righe di Echelon.
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Passaggio 1.1
Perform the row operation R2=R2-R1R2=R2−R1 to make the entry at 2,12,1 a 00.
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Passaggio 1.1.1
Perform the row operation R2=R2-R1R2=R2−R1 to make the entry at 2,12,1 a 00.
[10011000001-11-01-00-10-10-00-00-00-00-001010000000102100000110000000000101000000010000001000001000000000111100000001100]⎡⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢⎣10011000001−11−01−00−10−10−00−00−00−00−001010000000102100000110000000000101000000010000001000001000000000111100000001100⎤⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥⎦
Passaggio 1.1.2
Semplifica R2R2.
[1001100000011-1-10000001010000000102100000110000000000101000000010000001000001000000000111100000001100]⎡⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢⎣1001100000011−1−10000001010000000102100000110000000000101000000010000001000001000000000111100000001100⎤⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥⎦
[1001100000011-1-10000001010000000102100000110000000000101000000010000001000001000000000111100000001100]⎡⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢⎣1001100000011−1−10000001010000000102100000110000000000101000000010000001000001000000000111100000001100⎤⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥⎦
Passaggio 1.2
Perform the row operation R5=R5-R1R5=R5−R1 to make the entry at 5,15,1 a 00.
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Passaggio 1.2.1
Perform the row operation R5=R5-R1R5=R5−R1 to make the entry at 5,15,1 a 00.
[1001100000011-1-100000010100000001021000001-11-00-00-10-10-00-00-00-00-000101000000010000001000001000000000111100000001100]⎡⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢⎣1001100000011−1−100000010100000001021000001−11−00−00−10−10−00−00−00−00−000101000000010000001000001000000000111100000001100⎤⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥⎦
Passaggio 1.2.2
Semplifica R5R5.
[1001100000011-1-10000001010000000102100000010-1-10000000101000000010000001000001000000000111100000001100]⎡⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢⎣1001100000011−1−10000001010000000102100000010−1−10000000101000000010000001000001000000000111100000001100⎤⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥⎦
[1001100000011-1-10000001010000000102100000010-1-10000000101000000010000001000001000000000111100000001100]⎡⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢⎣1001100000011−1−10000001010000000102100000010−1−10000000101000000010000001000001000000000111100000001100⎤⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥⎦
Passaggio 1.3
Perform the row operation R3=R3-R2R3=R3−R2 to make the entry at 3,23,2 a 00.
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Passaggio 1.3.1
Perform the row operation R3=R3-R2R3=R3−R2 to make the entry at 3,23,2 a 00.
[1001100000011-1-1000000-01-10-11+10+10-00-00-00-00-00102100000010-1-10000000101000000010000001000001000000000111100000001100]⎡⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢⎣1001100000011−1−1000000−01−10−11+10+10−00−00−00−00−00102100000010−1−10000000101000000010000001000001000000000111100000001100⎤⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥⎦
Passaggio 1.3.2
Semplifica R3R3.
[1001100000011-1-10000000-121000000102100000010-1-10000000101000000010000001000001000000000111100000001100]⎡⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢⎣1001100000011−1−10000000−121000000102100000010−1−10000000101000000010000001000001000000000111100000001100⎤⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥⎦
[1001100000011-1-10000000-121000000102100000010-1-10000000101000000010000001000001000000000111100000001100]⎡⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢⎣1001100000011−1−10000000−121000000102100000010−1−10000000101000000010000001000001000000000111100000001100⎤⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥⎦
Passaggio 1.4
Perform the row operation R4=R4-R2R4=R4−R2 to make the entry at 4,24,2 a 00.
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Passaggio 1.4.1
Perform the row operation R4=R4-R2R4=R4−R2 to make the entry at 4,24,2 a 00.
[1001100000011-1-10000000-121000000-01-10-12+11+10-00-00-00-00-0010-1-10000000101000000010000001000001000000000111100000001100]⎡⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢⎣1001100000011−1−10000000−121000000−01−10−12+11+10−00−00−00−00−0010−1−10000000101000000010000001000001000000000111100000001100⎤⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥⎦
Passaggio 1.4.2
Semplifica R4R4.
[1001100000011-1-10000000-1210000000-13200000010-1-10000000101000000010000001000001000000000111100000001100]⎡⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢⎣1001100000011−1−10000000−1210000000−13200000010−1−10000000101000000010000001000001000000000111100000001100⎤⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥⎦
[1001100000011-1-10000000-1210000000-13200000010-1-10000000101000000010000001000001000000000111100000001100]⎡⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢⎣1001100000011−1−10000000−1210000000−13200000010−1−10000000101000000010000001000001000000000111100000001100⎤⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥⎦
Passaggio 1.5
Perform the row operation R5=R5-R2R5=R5−R2 to make the entry at 5,25,2 a 00.
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Passaggio 1.5.1
Perform the row operation R5=R5-R2R5=R5−R2 to make the entry at 5,25,2 a 00.
[1001100000011-1-10000000-1210000000-132000000-01-10-1-1+1-1+10-00-00-00-00-000101000000010000001000001000000000111100000001100]⎡⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢⎣1001100000011−1−10000000−1210000000−132000000−01−10−1−1+1−1+10−00−00−00−00−000101000000010000001000001000000000111100000001100⎤⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥⎦
Passaggio 1.5.2
Semplifica R5R5.
[1001100000011-1-10000000-1210000000-1320000000-1000000000101000000010000001000001000000000111100000001100]⎡⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢⎣1001100000011−1−10000000−1210000000−1320000000−1000000000101000000010000001000001000000000111100000001100⎤⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥⎦
[1001100000011-1-10000000-1210000000-1320000000-1000000000101000000010000001000001000000000111100000001100]⎡⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢⎣1001100000011−1−10000000−1210000000−1320000000−1000000000101000000010000001000001000000000111100000001100⎤⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥⎦
Passaggio 1.6
Multiply each element of R3R3 by -1−1 to make the entry at 3,33,3 a 11.
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Passaggio 1.6.1
Multiply each element of R3R3 by -1−1 to make the entry at 3,33,3 a 11.
[1001100000011-1-100000-0-0--1-1⋅2-1⋅1-0-0-0-0-000-1320000000-1000000000101000000010000001000001000000000111100000001100]⎡⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢⎣1001100000011−1−100000−0−0−−1−1⋅2−1⋅1−0−0−0−0−000−1320000000−1000000000101000000010000001000001000000000111100000001100⎤⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥⎦
Passaggio 1.6.2
Semplifica R3R3.
[1001100000011-1-100000001-2-10000000-1320000000-1000000000101000000010000001000001000000000111100000001100]⎡⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢⎣1001100000011−1−100000001−2−10000000−1320000000−1000000000101000000010000001000001000000000111100000001100⎤⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥⎦
[1001100000011-1-100000001-2-10000000-1320000000-1000000000101000000010000001000001000000000111100000001100]⎡⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢⎣1001100000011−1−100000001−2−10000000−1320000000−1000000000101000000010000001000001000000000111100000001100⎤⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥⎦
Passaggio 1.7
Perform the row operation R4=R4+R3R4=R4+R3 to make the entry at 4,34,3 a 00.
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Passaggio 1.7.1
Perform the row operation R4=R4+R3R4=R4+R3 to make the entry at 4,34,3 a 00.
[1001100000011-1-100000001-2-1000000+00+0-1+1⋅13-22-10+00+00+00+00+000-1000000000101000000010000001000001000000000111100000001100]⎡⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢⎣1001100000011−1−100000001−2−1000000+00+0−1+1⋅13−22−10+00+00+00+00+000−1000000000101000000010000001000001000000000111100000001100⎤⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥⎦
Passaggio 1.7.2
Semplifica R4R4.
[1001100000011-1-100000001-2-100000000110000000-1000000000101000000010000001000001000000000111100000001100]⎡⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢⎣1001100000011−1−100000001−2−100000000110000000−1000000000101000000010000001000001000000000111100000001100⎤⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥⎦
[1001100000011-1-100000001-2-100000000110000000-1000000000101000000010000001000001000000000111100000001100]⎡⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢⎣1001100000011−1−100000001−2−100000000110000000−1000000000101000000010000001000001000000000111100000001100⎤⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥⎦
Passaggio 1.8
Perform the row operation R5=R5+R3R5=R5+R3 to make the entry at 5,35,3 a 00.
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Passaggio 1.8.1
Perform the row operation R5=R5+R3R5=R5+R3 to make the entry at 5,35,3 a 00.
[1001100000011-1-100000001-2-10000000011000000+00+0-1+1⋅10-20-10+00+00+00+00+000101000000010000001000001000000000111100000001100]⎡⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢⎣1001100000011−1−100000001−2−10000000011000000+00+0−1+1⋅10−20−10+00+00+00+00+000101000000010000001000001000000000111100000001100⎤⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥⎦
Passaggio 1.8.2
Semplifica R5R5.
[1001100000011-1-100000001-2-1000000001100000000-2-10000000101000000010000001000001000000000111100000001100]⎡⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢⎣1001100000011−1−100000001−2−1000000001100000000−2−10000000101000000010000001000001000000000111100000001100⎤⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥⎦
[1001100000011-1-100000001-2-1000000001100000000-2-10000000101000000010000001000001000000000111100000001100]⎡⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢⎣1001100000011−1−100000001−2−1000000001100000000−2−10000000101000000010000001000001000000000111100000001100⎤⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥⎦
Passaggio 1.9
Perform the row operation R6=R6-R3R6=R6−R3 to make the entry at 6,36,3 a 00.
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Passaggio 1.9.1
Perform the row operation R6=R6-R3R6=R6−R3 to make the entry at 6,36,3 a 00.
[1001100000011-1-100000001-2-1000000001100000000-2-1000000-00-01-10+21+10-00-00-00-00-00010000001000001000000000111100000001100]⎡⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢⎣1001100000011−1−100000001−2−1000000001100000000−2−1000000−00−01−10+21+10−00−00−00−00−00010000001000001000000000111100000001100⎤⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥⎦
Passaggio 1.9.2
Semplifica R6R6.
[1001100000011-1-100000001-2-1000000001100000000-2-10000000022000000010000001000001000000000111100000001100]⎡⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢⎣1001100000011−1−100000001−2−1000000001100000000−2−10000000022000000010000001000001000000000111100000001100⎤⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥⎦
[1001100000011-1-100000001-2-1000000001100000000-2-10000000022000000010000001000001000000000111100000001100]⎡⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢⎣1001100000011−1−100000001−2−1000000001100000000−2−10000000022000000010000001000001000000000111100000001100⎤⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥⎦
Passaggio 1.10
Perform the row operation R7=R7-R3R7=R7−R3 to make the entry at 7,37,3 a 00.
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Passaggio 1.10.1
Perform the row operation R7=R7-R3R7=R7−R3 to make the entry at 7,37,3 a 00.
[1001100000011-1-100000001-2-1000000001100000000-2-10000000022000000-00-01-10+20+10-00-00-00-01-0000001000000000111100000001100]⎡⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢⎣1001100000011−1−100000001−2−1000000001100000000−2−10000000022000000−00−01−10+20+10−00−00−00−01−0000001000000000111100000001100⎤⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥⎦
Passaggio 1.10.2
Semplifica R7R7.
[1001100000011-1-100000001-2-1000000001100000000-2-10000000022000000002100001000001000000000111100000001100]⎡⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢⎣1001100000011−1−100000001−2−1000000001100000000−2−10000000022000000002100001000001000000000111100000001100⎤⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥⎦
[1001100000011-1-100000001-2-1000000001100000000-2-10000000022000000002100001000001000000000111100000001100]⎡⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢⎣1001100000011−1−100000001−2−1000000001100000000−2−10000000022000000002100001000001000000000111100000001100⎤⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥⎦
Passaggio 1.11
Perform the row operation R5=R5+2R4R5=R5+2R4 to make the entry at 5,45,4 a 00.
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Passaggio 1.11.1
Perform the row operation R5=R5+2R4R5=R5+2R4 to make the entry at 5,45,4 a 00.
[1001100000011-1-100000001-2-10000000011000000+2⋅00+2⋅00+2⋅0-2+2⋅1-1+2⋅10+2⋅00+2⋅00+2⋅00+2⋅00+2⋅000022000000002100001000001000000000111100000001100]⎡⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢⎣1001100000011−1−100000001−2−10000000011000000+2⋅00+2⋅00+2⋅0−2+2⋅1−1+2⋅10+2⋅00+2⋅00+2⋅00+2⋅00+2⋅000022000000002100001000001000000000111100000001100⎤⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥⎦
Passaggio 1.11.2
Semplifica R5R5.
[1001100000011-1-100000001-2-1000000001100000000010000000022000000002100001000001000000000111100000001100]⎡⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢⎣1001100000011−1−100000001−2−1000000001100000000010000000022000000002100001000001000000000111100000001100⎤⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥⎦
[1001100000011-1-100000001-2-1000000001100000000010000000022000000002100001000001000000000111100000001100]⎡⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢⎣1001100000011−1−100000001−2−1000000001100000000010000000022000000002100001000001000000000111100000001100⎤⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥⎦
Passaggio 1.12
Perform the row operation R6=R6-2R4R6=R6−2R4 to make the entry at 6,46,4 a 00.
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Passaggio 1.12.1
Perform the row operation R6=R6-2R4R6=R6−2R4 to make the entry at 6,46,4 a 00.
[1001100000011-1-100000001-2-100000000110000000001000000-2⋅00-2⋅00-2⋅02-2⋅12-2⋅10-2⋅00-2⋅00-2⋅00-2⋅00-2⋅00002100001000001000000000111100000001100]⎡⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢⎣1001100000011−1−100000001−2−100000000110000000001000000−2⋅00−2⋅00−2⋅02−2⋅12−2⋅10−2⋅00−2⋅00−2⋅00−2⋅00−2⋅00002100001000001000000000111100000001100⎤⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥⎦
Passaggio 1.12.2
Semplifica R6R6.
[1001100000011-1-100000001-2-1000000001100000000010000000000000000002100001000001000000000111100000001100]⎡⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢⎣1001100000011−1−100000001−2−1000000001100000000010000000000000000002100001000001000000000111100000001100⎤⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥⎦
[1001100000011-1-100000001-2-1000000001100000000010000000000000000002100001000001000000000111100000001100]⎡⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢⎣1001100000011−1−100000001−2−1000000001100000000010000000000000000002100001000001000000000111100000001100⎤⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥⎦
Passaggio 1.13
Perform the row operation R7=R7-2R4R7=R7−2R4 to make the entry at 7,47,4 a 00.
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Passaggio 1.13.1
Perform the row operation R7=R7-2R4R7=R7−2R4 to make the entry at 7,47,4 a 00.
[1001100000011-1-100000001-2-1000000001100000000010000000000000000-2⋅00-2⋅00-2⋅02-2⋅11-2⋅10-2⋅00-2⋅00-2⋅00-2⋅01-2⋅0000001000000000111100000001100]⎡⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢⎣1001100000011−1−100000001−2−1000000001100000000010000000000000000−2⋅00−2⋅00−2⋅02−2⋅11−2⋅10−2⋅00−2⋅00−2⋅00−2⋅01−2⋅0000001000000000111100000001100⎤⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥⎦
Passaggio 1.13.2
Semplifica R7R7.
[1001100000011-1-100000001-2-1000000001100000000010000000000000000000-100001000001000000000111100000001100]⎡⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢⎣1001100000011−1−100000001−2−1000000001100000000010000000000000000000−100001000001000000000111100000001100⎤⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥⎦
[1001100000011-1-100000001-2-1000000001100000000010000000000000000000-100001000001000000000111100000001100]⎡⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢⎣1001100000011−1−100000001−2−1000000001100000000010000000000000000000−100001000001000000000111100000001100⎤⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥⎦
Passaggio 1.14
Perform the row operation R7=R7+R5R7=R7+R5 to make the entry at 7,57,5 a 00.
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Passaggio 1.14.1
Perform the row operation R7=R7+R5R7=R7+R5 to make the entry at 7,57,5 a 00.
[1001100000011-1-100000001-2-1000000001100000000010000000000000000+00+00+00+0-1+1⋅10+00+00+00+01+0000001000000000111100000001100]⎡⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢⎣1001100000011−1−100000001−2−1000000001100000000010000000000000000+00+00+00+0−1+1⋅10+00+00+00+01+0000001000000000111100000001100⎤⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥⎦
Passaggio 1.14.2
Semplifica R7R7.
[1001100000011-1-100000001-2-1000000001100000000010000000000000000000000001000001000000000111100000001100]⎡⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢⎣1001100000011−1−100000001−2−1000000001100000000010000000000000000000000001000001000000000111100000001100⎤⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥⎦
[1001100000011-1-100000001-2-1000000001100000000010000000000000000000000001000001000000000111100000001100]⎡⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢⎣1001100000011−1−100000001−2−1000000001100000000010000000000000000000000001000001000000000111100000001100⎤⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥⎦
Passaggio 1.15
Swap R8R8 with R6R6 to put a nonzero entry at 6,66,6.
[1001100000011-1-100000001-2-1000000001100000000010000000000100000000000001000000000000000111100000001100]⎡⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢⎣1001100000011−1−100000001−2−1000000001100000000010000000000100000000000001000000000000000111100000001100⎤⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥⎦
Passaggio 1.16
Perform the row operation R9=R9-R6R9=R9−R6 to make the entry at 9,69,6 a 00.
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Passaggio 1.16.1
Perform the row operation R9=R9-R6R9=R9−R6 to make the entry at 9,69,6 a 00.
[1001100000011-1-100000001-2-100000000110000000001000000000010000000000000100000000000-00-00-00-00-01-11-01-01-00-00000001100]⎡⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢⎣1001100000011−1−100000001−2−100000000110000000001000000000010000000000000100000000000−00−00−00−00−01−11−01−01−00−00000001100⎤⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥⎦
Passaggio 1.16.2
Semplifica R9R9.
[1001100000011-1-100000001-2-1000000001100000000010000000000100000000000001000000000000000011100000001100]⎡⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢⎣1001100000011−1−100000001−2−1000000001100000000010000000000100000000000001000000000000000011100000001100⎤⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥⎦
[1001100000011-1-100000001-2-1000000001100000000010000000000100000000000001000000000000000011100000001100]⎡⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢⎣1001100000011−1−100000001−2−1000000001100000000010000000000100000000000001000000000000000011100000001100⎤⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥⎦
Passaggio 1.17
Swap R9R9 with R7R7 to put a nonzero entry at 7,77,7.
[1001100000011-1-100000001-2-1000000001100000000010000000000100000000001110000000000000000000010000001100]⎡⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢⎣1001100000011−1−100000001−2−1000000001100000000010000000000100000000001110000000000000000000010000001100⎤⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥⎦
Passaggio 1.18
Perform the row operation R10=R10-R7R10=R10−R7 to make the entry at 10,710,7 a 00.
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Passaggio 1.18.1
Perform the row operation R10=R10-R7R10=R10−R7 to make the entry at 10,710,7 a 00.
[1001100000011-1-100000001-2-1000000001100000000010000000000100000000001110000000000000000000010-00-00-00-00-00-01-11-10-10-0]⎡⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢⎣1001100000011−1−100000001−2−1000000001100000000010000000000100000000001110000000000000000000010−00−00−00−00−00−01−11−10−10−0⎤⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥⎦
Passaggio 1.18.2
Semplifica R10R10.
[1001100000011-1-100000001-2-10000000011000000000100000000001000000000011100000000000000000000100000000-10]⎡⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢⎣1001100000011−1−100000001−2−10000000011000000000100000000001000000000011100000000000000000000100000000−10⎤⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥⎦
[1001100000011-1-100000001-2-10000000011000000000100000000001000000000011100000000000000000000100000000-10]⎡⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢⎣1001100000011−1−100000001−2−10000000011000000000100000000001000000000011100000000000000000000100000000−10⎤⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥⎦
Passaggio 1.19
Swap R10R10 with R8R8 to put a nonzero entry at 8,98,9.
[1001100000011-1-100000001-2-100000000110000000001000000000010000000000111000000000-1000000000010000000000]⎡⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢⎣1001100000011−1−100000001−2−100000000110000000001000000000010000000000111000000000−1000000000010000000000⎤⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥⎦
Passaggio 1.20
Multiply each element of R8R8 by -1−1 to make the entry at 8,98,9 a 11.
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Passaggio 1.20.1
Multiply each element of R8R8 by -1−1 to make the entry at 8,98,9 a 11.
[1001100000011-1-100000001-2-1000000001100000000010000000000100000000001110-0-0-0-0-0-0-0-0--1-000000000010000000000]⎡⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢⎣1001100000011−1−100000001−2−1000000001100000000010000000000100000000001110−0−0−0−0−0−0−0−0−−1−000000000010000000000⎤⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥⎦
Passaggio 1.20.2
Semplifica R8R8.
[1001100000011-1-100000001-2-1000000001100000000010000000000100000000001110000000001000000000010000000000]⎡⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢⎣1001100000011−1−100000001−2−1000000001100000000010000000000100000000001110000000001000000000010000000000⎤⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥⎦
[1001100000011-1-100000001-2-1000000001100000000010000000000100000000001110000000001000000000010000000000]⎡⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢⎣1001100000011−1−100000001−2−1000000001100000000010000000000100000000001110000000001000000000010000000000⎤⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥⎦
Passaggio 1.21
Perform the row operation R7=R7-R8R7=R7−R8 to make the entry at 7,97,9 a 00.
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Passaggio 1.21.1
Perform the row operation R7=R7-R8R7=R7−R8 to make the entry at 7,97,9 a 00.
[1001100000011-1-100000001-2-1000000001100000000010000000000100000-00-00-00-00-00-01-01-01-10-0000000001000000000010000000000]⎡⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢⎣1001100000011−1−100000001−2−1000000001100000000010000000000100000−00−00−00−00−00−01−01−01−10−0000000001000000000010000000000⎤⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥⎦
Passaggio 1.21.2
Semplifica R7R7.
[1001100000011-1-100000001-2-1000000001100000000010000000000100000000001100000000001000000000010000000000]⎡⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢⎣1001100000011−1−100000001−2−1000000001100000000010000000000100000000001100000000001000000000010000000000⎤⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥⎦
[1001100000011-1-100000001-2-1000000001100000000010000000000100000000001100000000001000000000010000000000]
Passaggio 1.22
Perform the row operation R4=R4-R5 to make the entry at 4,5 a 0.
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Passaggio 1.22.1
Perform the row operation R4=R4-R5 to make the entry at 4,5 a 0.
[1001100000011-1-100000001-2-1000000-00-00-01-01-10-00-00-00-00-0000010000000000100000000001100000000001000000000010000000000]
Passaggio 1.22.2
Semplifica R4.
[1001100000011-1-100000001-2-1000000001000000000010000000000100000000001100000000001000000000010000000000]
[1001100000011-1-100000001-2-1000000001000000000010000000000100000000001100000000001000000000010000000000]
Passaggio 1.23
Perform the row operation R3=R3+R5 to make the entry at 3,5 a 0.
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Passaggio 1.23.1
Perform the row operation R3=R3+R5 to make the entry at 3,5 a 0.
[1001100000011-1-1000000+00+01+0-2+0-1+1⋅10+00+00+00+00+00001000000000010000000000100000000001100000000001000000000010000000000]
Passaggio 1.23.2
Semplifica R3.
[1001100000011-1-100000001-20000000001000000000010000000000100000000001100000000001000000000010000000000]
[1001100000011-1-100000001-20000000001000000000010000000000100000000001100000000001000000000010000000000]
Passaggio 1.24
Perform the row operation R2=R2+R5 to make the entry at 2,5 a 0.
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Passaggio 1.24.1
Perform the row operation R2=R2+R5 to make the entry at 2,5 a 0.
[10011000000+01+01+0-1+0-1+1⋅10+00+00+00+00+0001-20000000001000000000010000000000100000000001100000000001000000000010000000000]
Passaggio 1.24.2
Semplifica R2.
[1001100000011-1000000001-20000000001000000000010000000000100000000001100000000001000000000010000000000]
[1001100000011-1000000001-20000000001000000000010000000000100000000001100000000001000000000010000000000]
Passaggio 1.25
Perform the row operation R1=R1-R5 to make the entry at 1,5 a 0.
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Passaggio 1.25.1
Perform the row operation R1=R1-R5 to make the entry at 1,5 a 0.
[1-00-00-01-01-10-00-00-00-00-0011-1000000001-20000000001000000000010000000000100000000001100000000001000000000010000000000]
Passaggio 1.25.2
Semplifica R1.
[1001000000011-1000000001-20000000001000000000010000000000100000000001100000000001000000000010000000000]
[1001000000011-1000000001-20000000001000000000010000000000100000000001100000000001000000000010000000000]
Passaggio 1.26
Perform the row operation R3=R3+2R4 to make the entry at 3,4 a 0.
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Passaggio 1.26.1
Perform the row operation R3=R3+2R4 to make the entry at 3,4 a 0.
[1001000000011-10000000+2⋅00+2⋅01+2⋅0-2+2⋅10+2⋅00+2⋅00+2⋅00+2⋅00+2⋅00+2⋅00001000000000010000000000100000000001100000000001000000000010000000000]
Passaggio 1.26.2
Semplifica R3.
[1001000000011-100000000100000000001000000000010000000000100000000001100000000001000000000010000000000]
[1001000000011-100000000100000000001000000000010000000000100000000001100000000001000000000010000000000]
Passaggio 1.27
Perform the row operation R2=R2+R4 to make the entry at 2,4 a 0.
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Passaggio 1.27.1
Perform the row operation R2=R2+R4 to make the entry at 2,4 a 0.
[10010000000+01+01+0-1+1⋅10+00+00+00+00+00+000100000000001000000000010000000000100000000001100000000001000000000010000000000]
Passaggio 1.27.2
Semplifica R2.
[1001000000011000000000100000000001000000000010000000000100000000001100000000001000000000010000000000]
[1001000000011000000000100000000001000000000010000000000100000000001100000000001000000000010000000000]
Passaggio 1.28
Perform the row operation R1=R1-R4 to make the entry at 1,4 a 0.
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Passaggio 1.28.1
Perform the row operation R1=R1-R4 to make the entry at 1,4 a 0.
[1-00-00-01-10-00-00-00-00-00-0011000000000100000000001000000000010000000000100000000001100000000001000000000010000000000]
Passaggio 1.28.2
Semplifica R1.
[1000000000011000000000100000000001000000000010000000000100000000001100000000001000000000010000000000]
[1000000000011000000000100000000001000000000010000000000100000000001100000000001000000000010000000000]
Passaggio 1.29
Perform the row operation R2=R2-R3 to make the entry at 2,3 a 0.
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Passaggio 1.29.1
Perform the row operation R2=R2-R3 to make the entry at 2,3 a 0.
[10000000000-01-01-10-00-00-00-00-00-00-000100000000001000000000010000000000100000000001100000000001000000000010000000000]
Passaggio 1.29.2
Semplifica R2.
[1000000000010000000000100000000001000000000010000000000100000000001100000000001000000000010000000000]
[1000000000010000000000100000000001000000000010000000000100000000001100000000001000000000010000000000]
[1000000000010000000000100000000001000000000010000000000100000000001100000000001000000000010000000000]
Passaggio 2
The pivot positions are the locations with the leading 1 in each row. The pivot columns are the columns that have a pivot position.
Pivot Positions: a11,a22,a33,a44,a55,a66,a77,a89, and a910
Pivot Columns: 1,2,3,4,5,6,7,9, and 10
Passaggio 3
The rank is the number of pivot columns.
9
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