Resolva um sistema de equa\303\247\303\265es com as matrizes elementares.Xhumga bernard Amadora em matem\303\241tica e linguagem C. Iniciante no bordo 15.Maple Cloud : mathc

Neste trabalho, tentei usar as matrizes elementares para resolver um sistema de equa\303\247\303\265es. A vers\303\243o A usa uma matriz P para definir o piv\303\264 para "1". (M: = P.M;) Ent\303\243o eu modifico essa matriz para colocar em "0" todos os coeficientes abaixo do piv\303\264. (M: = P.M;) A vers\303\243o B usa duas matrizes P1 e P2. P1 para definir o piv\303\264 para "1". P2 para definir todos os coeficientes no piv\303\264 para "0". (M: = P2.P1.M;) A vers\303\243o C usa um dado \303\272nico que faz todo o trabalho. (M: = P.M;) Para encontrar essa matriz, simplesmente multipliquei P2 e P1 da vers\303\243o B. (P: = P2.P1;)

restart: with(Student[LinearAlgebra]): randomize(): A := RandomMatrix(3, 4): M := A;

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSJNR0YoLUknUlRBQkxFR0YoNiUiNWVwJmVdR2x1WSU9LUknTUFUUklYR0YoNiM3JTcmLUkjbW5HNiRGJi9JK21vZHVsZW5hbWVHRihGJDYjUSMxNkYoLUY4NiNRLCZ1bWludXMwOzI5RigtRjg2I1EjMjdGKC1GODYjUSwmdW1pbnVzMDs4NkYoNyYtRjg2I1EjNzZGKC1GODYjUSM4N0YoLUY4NiNRIzI1RigtRjg2I1EsJnVtaW51czA7MThGKDcmLUY4NiNRIzQ0RigtRjg2I1EjNzFGKC1GODYjUSwmdW1pbnVzMDs1MEYoLUY4NiNRLCZ1bWludXMwOzM0RihJJ01hdHJpeEdGJTcjLUZbbzYjL0kkJWlkR0YoRjE=

restart: with(Student[LinearAlgebra]): A := Matrix(3,4, [ -2, 31,-91,-50, 66,-53,-96,-29, 57, 74,-23, 58]): M := A;

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSJNR0YoLUknUlRBQkxFR0YoNiUiNWVwJmVdR2x1WSU9LUknTUFUUklYR0YoNiM3JTcmLUkjbW5HNiRGJi9JK21vZHVsZW5hbWVHRihGJDYjUSsmdW1pbnVzMDsyRigtRjg2I1EjMzFGKC1GODYjUSwmdW1pbnVzMDs5MUYoLUY4NiNRLCZ1bWludXMwOzUwRig3Ji1GODYjUSM2NkYoLUY4NiNRLCZ1bWludXMwOzUzRigtRjg2I1EsJnVtaW51czA7OTZGKC1GODYjUSwmdW1pbnVzMDsyOUYoNyYtRjg2I1EjNTdGKC1GODYjUSM3NEYoLUY4NiNRLCZ1bWludXMwOzIzRigtRjg2I1EjNThGKEknTWF0cml4R0YlNyMtRltvNiMvSSQlaWRHRihGMQ==

P := Matrix(3,3, [ -1/2, 0, 0, 0, 1, 0, 0, 0, 1 ]): M := P.M;

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

P := Matrix(3,3, [ 1, 0, 0, -66, 1, 0, -57, 0, 1 ]): M := P.M;

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

P := Matrix(3,3, [ 1, 0, 0, 0, 1/970, 0, 0, 0, 1 ]): M := P.M;

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

P := Matrix(3,3, [ 1, 0, 0, 0, 1, 0, 0, -1915/2, 1 ]): M := P.M;

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

P := Matrix(3,3, [ 1, 0, 0, 0, 1, 0, 0, 0, 1/(171715/388) ]): M := P.M;

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

P := Matrix(3,3, [ 1, 0, -91/2, 0, 1, 3099/970, 0, 0, 1 ]): M := P.M;

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P := Matrix(3,3, [ 1, 31/2, 0, 0, 1, 0, 0, 0, 1 ]): M := P.M;

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSJNR0YoLUknUlRBQkxFR0YoNiUiNSdvInBVJkdsdVklPS1JJ01BVFJJWEdGKDYjNyU3Ji1JI21uRzYkRiYvSSttb2R1bGVuYW1lR0YoRiQ2I1EiMUYoLUY4NiNRIjBGKEY+LUkmbWZyYWNHRjk2JC1GODYjUSc2OTM4ODNGKC1GODYjUSc4NTg1NzVGKDcmRj5GN0Y+LUZCNiQtRjg2I1EnMzEzNTQxRihGRzcmRj5GPkY3LUZCNiQtRjg2I1EnMTEyNjYxRigtRjg2I1EnMTcxNzE1RihJJ01hdHJpeEdGJTcjLUZZNiMvSSQlaWRHRihGMQ==

ReducedRowEchelonForm(A);

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyMtSSdSVEFCTEVHRig2JSI1J28lcFUmR2x1WSU9LUknTUFUUklYR0YoNiM3JTcmLUkjbW5HNiRGJi9JK21vZHVsZW5hbWVHRihGJDYjUSIxRigtRjY2I1EiMEYoRjwtSSZtZnJhY0dGNzYkLUY2NiNRJzY5Mzg4M0YoLUY2NiNRJzg1ODU3NUYoNyZGPEY1RjwtRkA2JC1GNjYjUSczMTM1NDFGKEZFNyZGPEY8RjUtRkA2JC1GNjYjUScxMTI2NjFGKC1GNjYjUScxNzE3MTVGKEknTWF0cml4R0YlNyMtRlc2Iy9JJCVpZEdGKEYv

restart: with(Student[LinearAlgebra]): A := Matrix(3,4, [-65, 31,-91,-50, 66,-53,-96,-29, 57, 74,-23, 58]): M := A;

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSJNR0YoLUknUlRBQkxFR0YoNiUiNWVwJmVdR2x1WSU9LUknTUFUUklYR0YoNiM3JTcmLUkjbW5HNiRGJi9JK21vZHVsZW5hbWVHRihGJDYjUSwmdW1pbnVzMDs2NUYoLUY4NiNRIzMxRigtRjg2I1EsJnVtaW51czA7OTFGKC1GODYjUSwmdW1pbnVzMDs1MEYoNyYtRjg2I1EjNjZGKC1GODYjUSwmdW1pbnVzMDs1M0YoLUY4NiNRLCZ1bWludXMwOzk2RigtRjg2I1EsJnVtaW51czA7MjlGKDcmLUY4NiNRIzU3RigtRjg2I1EjNzRGKC1GODYjUSwmdW1pbnVzMDsyM0YoLUY4NiNRIzU4RihJJ01hdHJpeEdGJTcjLUZbbzYjL0kkJWlkR0YoRjE=

P := Matrix(3,3, [ 1/M[1,1], 0, 0, 0, 1, 0, 0, 0, 1 ]): M := P.M;

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

P := Matrix(3,3, [ 1, 0, 0, -M[2,1], 1, 0, -M[3,1], 0, 1 ]): M := P.M;

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

P := Matrix(3,3, [ 1, 0, 0, 0, 1/M[2,2], 0, 0, 0, 1 ]): M := P.M;

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

P := Matrix(3,3, [ 1, 0, 0, 0, 1, 0, 0, -M[3,2], 1 ]): M := P.M;

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

P := Matrix(3,3, [ 1, 0, 0, 0, 1, 0, 0, 0, 1/M[3,3] ]): M := P.M;

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

P := Matrix(3,3, [ 1, 0, -M[1,3], 0, 1, -M[2,3], 0, 0, 1 ]): M := P.M;

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

P := Matrix(3,3, [ 1, -M[1,2], 0, 0, 1, 0, 0, 0, 1 ]): M := P.M;

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSJNR0YoLUknUlRBQkxFR0YoNiUiNSdvInBVJkdsdVklPS1JJ01BVFJJWEdGKDYjNyU3Ji1JI21uRzYkRiYvSSttb2R1bGVuYW1lR0YoRiQ2I1EiMUYoLUY4NiNRIjBGKEY+LUkmbWZyYWNHRjk2JC1GODYjUSc2OTM4ODNGKC1GODYjUSgxMzgyOTI0Rig3JkY+RjdGPi1GQjYkLUY4NiNRJzM1MzE3M0YoLUY4NiNRJzY5MTQ2MkYoNyZGPkY+RjctRkI2JC1GODYjUSc1MDQ4NDFGKEZHSSdNYXRyaXhHRiU3Iy1GWTYjL0kkJWlkR0YoRjE=

ReducedRowEchelonForm(A);

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyMtSSdSVEFCTEVHRig2JSI1J28lcFUmR2x1WSU9LUknTUFUUklYR0YoNiM3JTcmLUkjbW5HNiRGJi9JK21vZHVsZW5hbWVHRihGJDYjUSIxRigtRjY2I1EiMEYoRjwtSSZtZnJhY0dGNzYkLUY2NiNRJzY5Mzg4M0YoLUY2NiNRKDEzODI5MjRGKDcmRjxGNUY8LUZANiQtRjY2I1EnMzUzMTczRigtRjY2I1EnNjkxNDYyRig3JkY8RjxGNS1GQDYkLUY2NiNRJzUwNDg0MUYoRkVJJ01hdHJpeEdGJTcjLUZXNiMvSSQlaWRHRihGLw==

restart: with(Student[LinearAlgebra]): randomize(): A := RandomMatrix(3, 4): M := A;

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSJNR0YoLUknUlRBQkxFR0YoNiUiNWVwJmVdR2x1WSU9LUknTUFUUklYR0YoNiM3JTcmLUkjbW5HNiRGJi9JK21vZHVsZW5hbWVHRihGJDYjUSwmdW1pbnVzMDs5NkYoLUY4NiNRLCZ1bWludXMwOzIyRigtRjg2I1EjODlGKC1GODYjUSwmdW1pbnVzMDsxM0YoNyYtRjg2I1ErJnVtaW51czA7NkYoLUY4NiNRLCZ1bWludXMwOzYxRigtRjg2I1EsJnVtaW51czA7MThGKC1GODYjUSM0N0YoNyYtRjg2I1EsJnVtaW51czA7NTFGKC1GODYjUSM4MUYoLUY4NiNRIzYyRigtRjg2I1EjMTBGKEknTWF0cml4R0YlNyMtRltvNiMvSSQlaWRHRihGMQ==

P := Matrix(3,3, [ 1/M[1,1], 0, 0, 0, 1, 0, 0, 0, 1 ]): M := P.M;

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

P := Matrix(3,3, [ 1, 0, 0, -M[2,1], 1, 0, -M[3,1], 0, 1 ]): M := P.M;

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSJNR0YoLUknUlRBQkxFR0YoNiUiNXFpa1UmR2x1WSU9LUknTUFUUklYR0YoNiM3JTcmLUkjbW5HNiRGJi9JK21vZHVsZW5hbWVHRihGJDYjUSIxRigtSSZtZnJhY0dGOTYkLUY4NiNRIzExRigtRjg2I1EjNDhGKC1JJW1yb3dHRjk2JC1JI21vR0Y5NiNRKiZ1bWludXMwO0YoLUY/NiQtRjg2I1EjODlGKC1GODYjUSM5NkYoLUY/NiQtRjg2I1EjMTNGKEZTNyYtRjg2I1EiMEYoLUZINiRGSi1GPzYkLUY4NiNRJDQ3N0YoLUY4NiNRIjhGKC1GSDYkRkotRj82JC1GODYjUSQzNzdGKC1GODYjUSMxNkYoLUY/NiQtRjg2I1EkNzY1RihGam83JkZmbi1GPzYkLUY4NiNRJTE0ODNGKEZqby1GPzYkLUY4NiNRJDQ3MUYoLUY4NiNRIzMyRigtRj82JC1GODYjUSQ1NDFGKEZdcUknTWF0cml4R0YlNyMtRmVxNiMvSSQlaWRHRihGMQ==

P := Matrix(3,3, [ 1, 0, 0, 0, 1/M[2,2], 0, 0, 0, 1 ]): M := P.M;

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

P := Matrix(3,3, [ 1, 0, 0, 0, 1, 0, 0, -M[3,2], 1 ]): M := P.M;

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

P := Matrix(3,3, [ 1, 0, 0, 0, 1, 0, 0, 0, 1/M[3,3] ]): M := P.M;

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

P := Matrix(3,3, [ 1, 0, -M[1,3], 0, 1, -M[2,3], 0, 0, 1 ]): M := P.M;

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

P := Matrix(3,3, [ 1, -M[1,2], 0, 0, 1, 0, 0, 0, 1 ]): M := P.M;

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSJNR0YoLUknUlRBQkxFR0YoNiUiNVVWalUmR2x1WSU9LUknTUFUUklYR0YoNiM3JTcmLUkjbW5HNiRGJi9JK21vZHVsZW5hbWVHRihGJDYjUSIxRigtRjg2I1EiMEYoRj4tSSVtcm93R0Y5NiQtSSNtb0dGOTYjUSomdW1pbnVzMDtGKC1JJm1mcmFjR0Y5NiQtRjg2I1EnNDkxMzkzRigtRjg2I1EnMTI1NDA5Rig3JkY+RjdGPi1GSTYkLUY4NiNRJjM1MjY3RigtRjg2I1EmNDE4MDNGKDcmRj5GPkY3LUZCNiRGRC1GSTYkLUY4NiNRJzE3NDA2OUYoRldJJ01hdHJpeEdGJTcjLUZcbzYjL0kkJWlkR0YoRjE=

ReducedRowEchelonForm(A);

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyMtSSdSVEFCTEVHRig2JSI1VXRqVSZHbHVZJT0tSSdNQVRSSVhHRig2IzclNyYtSSNtbkc2JEYmL0krbW9kdWxlbmFtZUdGKEYkNiNRIjFGKC1GNjYjUSIwRihGPC1JJW1yb3dHRjc2JC1JI21vR0Y3NiNRKiZ1bWludXMwO0YoLUkmbWZyYWNHRjc2JC1GNjYjUSc0OTEzOTNGKC1GNjYjUScxMjU0MDlGKDcmRjxGNUY8LUZHNiQtRjY2I1EmMzUyNjdGKC1GNjYjUSY0MTgwM0YoNyZGPEY8RjUtRkA2JEZCLUZHNiQtRjY2I1EnMTc0MDY5RihGVUknTWF0cml4R0YlNyMtRmpuNiMvSSQlaWRHRihGLw==

restart: with(Student[LinearAlgebra]): A := Matrix(3,4, [-65, 31,-91,-50, 66,-53,-96,-29, 57, 74,-23, 58]): M := A;

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSJNR0YoLUknUlRBQkxFR0YoNiUiNWVwJmVdR2x1WSU9LUknTUFUUklYR0YoNiM3JTcmLUkjbW5HNiRGJi9JK21vZHVsZW5hbWVHRihGJDYjUSwmdW1pbnVzMDs2NUYoLUY4NiNRIzMxRigtRjg2I1EsJnVtaW51czA7OTFGKC1GODYjUSwmdW1pbnVzMDs1MEYoNyYtRjg2I1EjNjZGKC1GODYjUSwmdW1pbnVzMDs1M0YoLUY4NiNRLCZ1bWludXMwOzk2RigtRjg2I1EsJnVtaW51czA7MjlGKDcmLUY4NiNRIzU3RigtRjg2I1EjNzRGKC1GODYjUSwmdW1pbnVzMDsyM0YoLUY4NiNRIzU4RihJJ01hdHJpeEdGJTcjLUZbbzYjL0kkJWlkR0YoRjE=

P1 := Matrix(3,3, [ 1/M[1,1], 0, 0, 0, 1, 0, 0, 0, 1 ]): P2 := Matrix(3,3, [ 1, 0, 0, -M[2,1], 1, 0, -M[3,1], 0, 1 ]): M := P2.P1.M;

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

P1 := Matrix(3,3, [ 1, 0, 0, 0, 1/M[2,2], 0, 0, 0, 1 ]): P2 := Matrix(3,3, [ 1, 0, 0, 0, 1, 0, 0, -M[3,2], 1 ]): M := P2.P1.M;

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

P1 := Matrix(3,3, [ 1, 0, 0, 0, 1, 0, 0, 0, 1/M[3,3] ]): P2 := Matrix(3,3, [ 1, 0, -M[1,3], 0, 1, -M[2,3], 0, 0, 1 ]): M := P2.P1.M;

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

P := Matrix(3,3, [ 1, -M[1,2], 0, 0, 1, 0, 0, 0, 1 ]): M := P.M;

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSJNR0YoLUknUlRBQkxFR0YoNiUiNSk+LEZhR2x1WSU9LUknTUFUUklYR0YoNiM3JTcmLUkjbW5HNiRGJi9JK21vZHVsZW5hbWVHRihGJDYjUSIxRigtRjg2I1EiMEYoRj4tSSZtZnJhY0dGOTYkLUY4NiNRJzY5Mzg4M0YoLUY4NiNRKDEzODI5MjRGKDcmRj5GN0Y+LUZCNiQtRjg2I1EnMzUzMTczRigtRjg2I1EnNjkxNDYyRig3JkY+Rj5GNy1GQjYkLUY4NiNRJzUwNDg0MUYoRkdJJ01hdHJpeEdGJTcjLUZZNiMvSSQlaWRHRihGMQ==

ReducedRowEchelonForm(A);

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyMtSSdSVEFCTEVHRig2JSI1QWdwVSZHbHVZJT0tSSdNQVRSSVhHRig2IzclNyYtSSNtbkc2JEYmL0krbW9kdWxlbmFtZUdGKEYkNiNRIjFGKC1GNjYjUSIwRihGPC1JJm1mcmFjR0Y3NiQtRjY2I1EnNjkzODgzRigtRjY2I1EoMTM4MjkyNEYoNyZGPEY1RjwtRkA2JC1GNjYjUSczNTMxNzNGKC1GNjYjUSc2OTE0NjJGKDcmRjxGPEY1LUZANiQtRjY2I1EnNTA0ODQxRihGRUknTWF0cml4R0YlNyMtRlc2Iy9JJCVpZEdGKEYv

restart: with(Student[LinearAlgebra]): randomize(): A := RandomMatrix(3, 4): M := A;

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSJNR0YoLUknUlRBQkxFR0YoNiUiNWVwJmVdR2x1WSU9LUknTUFUUklYR0YoNiM3JTcmLUkjbW5HNiRGJi9JK21vZHVsZW5hbWVHRihGJDYjUSI5RigtRjg2I1EjNTBGKC1GODYjUSwmdW1pbnVzMDs0MkYoLUY4NiNRIjJGKDcmLUY4NiNRIzgxRigtRjg2I1EsJnVtaW51czA7MTVGKC1GODYjUSM1NEYoLUY4NiNRLCZ1bWludXMwOzM2Rig3Ji1GODYjUSwmdW1pbnVzMDsxNEYoLUY4NiNRIzUzRigtRjg2I1EjMjNGKC1GODYjUSwmdW1pbnVzMDs2M0YoSSdNYXRyaXhHRiU3Iy1GW282Iy9JJCVpZEdGKEYx

P1 := Matrix(3,3, [ 1/M[1,1], 0, 0, 0, 1, 0, 0, 0, 1 ]): P2 := Matrix(3,3, [ 1, 0, 0, -M[2,1], 1, 0, -M[3,1], 0, 1 ]): M := P2.P1.M;

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

P1 := Matrix(3,3, [ 1, 0, 0, 0, 1/M[2,2], 0, 0, 0, 1 ]): P2 := Matrix(3,3, [ 1, 0, 0, 0, 1, 0, 0, -M[3,2], 1 ]): M := P2.P1.M;

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

P1 := Matrix(3,3, [ 1, 0, 0, 0, 1, 0, 0, 0, 1/M[3,3] ]): P2 := Matrix(3,3, [ 1, 0, -M[1,3], 0, 1, -M[2,3], 0, 0, 1 ]): M := P2.P1.M;

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

P := Matrix(3,3, [ 1, -M[1,2], 0, 0, 1, 0, 0, 0, 1 ]): M := P.M;

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSJNR0YoLUknUlRBQkxFR0YoNiUiNWFRa1UmR2x1WSU9LUknTUFUUklYR0YoNiM3JTcmLUkjbW5HNiRGJi9JK21vZHVsZW5hbWVHRihGJDYjUSIxRigtRjg2I1EiMEYoRj4tSSZtZnJhY0dGOTYkLUY4NiNRJTUwOTZGKC1GODYjUScxMTA0MzNGKDcmRj5GN0Y+LUklbXJvd0dGOTYkLUkjbW9HRjk2I1EqJnVtaW51czA7RigtRkI2JC1GODYjUSYyODE1OEYoLUY4NiNRJjM2ODExRig3JkY+Rj5GNy1GTDYkRk4tRkI2JC1GODYjUScxMDQ3MzFGKEZHSSdNYXRyaXhHRiU3Iy1GXG82Iy9JJCVpZEdGKEYx

ReducedRowEchelonForm(A);

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyMtSSdSVEFCTEVHRig2JSI1eSdRRWFHbHVZJT0tSSdNQVRSSVhHRig2IzclNyYtSSNtbkc2JEYmL0krbW9kdWxlbmFtZUdGKEYkNiNRIjFGKC1GNjYjUSIwRihGPC1JJm1mcmFjR0Y3NiQtRjY2I1ElNTA5NkYoLUY2NiNRJzExMDQzM0YoNyZGPEY1RjwtSSVtcm93R0Y3NiQtSSNtb0dGNzYjUSomdW1pbnVzMDtGKC1GQDYkLUY2NiNRJjI4MTU4RigtRjY2I1EmMzY4MTFGKDcmRjxGPEY1LUZKNiRGTC1GQDYkLUY2NiNRJzEwNDczMUYoRkVJJ01hdHJpeEdGJTcjLUZqbjYjL0kkJWlkR0YoRi8=

restart: with(Student[LinearAlgebra]): A := Matrix(3,4, [-65, 31,-91,-50, 66,-53,-96,-29, 57, 74,-23, 58]): M := A;

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSJNR0YoLUknUlRBQkxFR0YoNiUiNWVwJmVdR2x1WSU9LUknTUFUUklYR0YoNiM3JTcmLUkjbW5HNiRGJi9JK21vZHVsZW5hbWVHRihGJDYjUSwmdW1pbnVzMDs2NUYoLUY4NiNRIzMxRigtRjg2I1EsJnVtaW51czA7OTFGKC1GODYjUSwmdW1pbnVzMDs1MEYoNyYtRjg2I1EjNjZGKC1GODYjUSwmdW1pbnVzMDs1M0YoLUY4NiNRLCZ1bWludXMwOzk2RigtRjg2I1EsJnVtaW51czA7MjlGKDcmLUY4NiNRIzU3RigtRjg2I1EjNzRGKC1GODYjUSwmdW1pbnVzMDsyM0YoLUY4NiNRIzU4RihJJ01hdHJpeEdGJTcjLUZbbzYjL0kkJWlkR0YoRjE=

P := Matrix(3,3, [ 1/M[1,1], 0, 0, -M[2,1]/M[1,1], 1, 0, -M[3,1]/M[1,1], 0, 1 ]): M := P.M;

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

P := Matrix(3,3, [ 1, 0, 0, 0, 1/M[2,2], 0, 0, -M[3,2]/M[2,2], 1 ]): M := P.M;

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

P := Matrix(3,3, [ 1, 0, -M[1,3]/M[3,3], 0, 1, -M[2,3]/M[3,3], 0, 0, 1/M[3,3] ]): M := P.M;

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

P := Matrix(3,3, [ 1, -M[1,2], 0, 0, 1, 0, 0, 0, 1 ]): M := P.M;

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSJNR0YoLUknUlRBQkxFR0YoNiUiNXkvcVUmR2x1WSU9LUknTUFUUklYR0YoNiM3JTcmLUkjbW5HNiRGJi9JK21vZHVsZW5hbWVHRihGJDYjUSIxRigtRjg2I1EiMEYoRj4tSSZtZnJhY0dGOTYkLUY4NiNRJzY5Mzg4M0YoLUY4NiNRKDEzODI5MjRGKDcmRj5GN0Y+LUZCNiQtRjg2I1EnMzUzMTczRigtRjg2I1EnNjkxNDYyRig3JkY+Rj5GNy1GQjYkLUY4NiNRJzUwNDg0MUYoRkdJJ01hdHJpeEdGJTcjLUZZNiMvSSQlaWRHRihGMQ==

ReducedRowEchelonForm(A);

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyMtSSdSVEFCTEVHRig2JSI1eU1xVSZHbHVZJT0tSSdNQVRSSVhHRig2IzclNyYtSSNtbkc2JEYmL0krbW9kdWxlbmFtZUdGKEYkNiNRIjFGKC1GNjYjUSIwRihGPC1JJm1mcmFjR0Y3NiQtRjY2I1EnNjkzODgzRigtRjY2I1EoMTM4MjkyNEYoNyZGPEY1RjwtRkA2JC1GNjYjUSczNTMxNzNGKC1GNjYjUSc2OTE0NjJGKDcmRjxGPEY1LUZANiQtRjY2I1EnNTA0ODQxRihGRUknTWF0cml4R0YlNyMtRlc2Iy9JJCVpZEdGKEYv

restart: with(Student[LinearAlgebra]): randomize(): A := RandomMatrix(3, 4): M := A;

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSJNR0YoLUknUlRBQkxFR0YoNiUiNWVwJmVdR2x1WSU9LUknTUFUUklYR0YoNiM3JTcmLUkjbW5HNiRGJi9JK21vZHVsZW5hbWVHRihGJDYjUSwmdW1pbnVzMDs0NUYoLUY4NiNRLCZ1bWludXMwOzU0RigtRjg2I1EsJnVtaW51czA7OTVGKC1GODYjUSwmdW1pbnVzMDs0NEYoNyYtRjg2I1EjODhGKC1GODYjUSM1MkYoLUY4NiNRIzI4RigtRjg2I1EsJnVtaW51czA7MjVGKDcmLUY4NiNRLCZ1bWludXMwOzE1RigtRjg2I1EjNjlGKC1GODYjUSwmdW1pbnVzMDs4MUYoLUY4NiNRIzE1RihJJ01hdHJpeEdGJTcjLUZbbzYjL0kkJWlkR0YoRjE=

P := Matrix(3,3, [ 1/M[1,1], 0, 0, -M[2,1]/M[1,1], 1, 0, -M[3,1]/M[1,1], 0, 1 ]): M := P.M;

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSJNR0YoLUknUlRBQkxFR0YoNiUiNUU+bFUmR2x1WSU9LUknTUFUUklYR0YoNiM3JTcmLUkjbW5HNiRGJi9JK21vZHVsZW5hbWVHRihGJDYjUSIxRigtSSZtZnJhY0dGOTYkLUY4NiNRIjZGKC1GODYjUSI1RigtRj82JC1GODYjUSMxOUYoLUY4NiNRIjlGKC1GPzYkLUY4NiNRIzQ0RigtRjg2I1EjNDVGKDcmLUY4NiNRIjBGKC1JJW1yb3dHRjk2JC1JI21vR0Y5NiNRKiZ1bWludXMwO0YoLUY/NiQtRjg2I1EkMjY4RihGRC1GZm42JEZobi1GPzYkLUY4NiNRJTE0MjBGKEZMLUZmbjYkRmhuLUY/NiQtRjg2I1ElNDk5N0YoRlQ3JkZYLUY4NiNRIzg3RigtRmZuNiRGaG4tRj82JC1GODYjUSQxNDhGKC1GODYjUSIzRigtRj82JC1GODYjUSM4OUYoRmpwSSdNYXRyaXhHRiU3Iy1GYnE2Iy9JJCVpZEdGKEYx

P := Matrix(3,3, [ 1, 0, 0, 0, 1/M[2,2], 0, 0, -M[3,2]/M[2,2], 1 ]): M := P.M;

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

P := Matrix(3,3, [ 1, 0, -M[1,3]/M[3,3], 0, 1, -M[2,3]/M[3,3], 0, 0, 1/M[3,3] ]): M := P.M;

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

P := Matrix(3,3, [ 1, -M[1,2], 0, 0, 1, 0, 0, 0, 1 ]): M := P.M;

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSJNR0YoLUknUlRBQkxFR0YoNiUiNU1Ka1UmR2x1WSU9LUknTUFUUklYR0YoNiM3JTcmLUkjbW5HNiRGJi9JK21vZHVsZW5hbWVHRihGJDYjUSIxRigtRjg2I1EiMEYoRj4tSSVtcm93R0Y5NiQtSSNtb0dGOTYjUSomdW1pbnVzMDtGKC1JJm1mcmFjR0Y5NiQtRjg2I1EnMTk4MzI3RigtRjg2I1EnMjQ1NTY0Rig3JkY+RjdGPi1GSTYkLUY4NiNRJjM4MDk2RigtRjg2I1EmNjEzOTFGKDcmRj5GPkY3LUZJNiQtRjg2I1EnMTIxMDYxRihGTkknTWF0cml4R0YlNyMtRmpuNiMvSSQlaWRHRihGMQ==

ReducedRowEchelonForm(A);

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyMtSSdSVEFCTEVHRig2JSI1TWhrVSZHbHVZJT0tSSdNQVRSSVhHRig2IzclNyYtSSNtbkc2JEYmL0krbW9kdWxlbmFtZUdGKEYkNiNRIjFGKC1GNjYjUSIwRihGPC1JJW1yb3dHRjc2JC1JI21vR0Y3NiNRKiZ1bWludXMwO0YoLUkmbWZyYWNHRjc2JC1GNjYjUScxOTgzMjdGKC1GNjYjUScyNDU1NjRGKDcmRjxGNUY8LUZHNiQtRjY2I1EmMzgwOTZGKC1GNjYjUSY2MTM5MUYoNyZGPEY8RjUtRkc2JC1GNjYjUScxMjEwNjFGKEZMSSdNYXRyaXhHRiU3Iy1GaG42Iy9JJCVpZEdGKEYv

O primeiro objetivo deste trabalho foi usar matrizes elementares para resolver um sistema de equa\303\247\303\265es. Ao introduzir o M [a, b] na matriz P, isso me permitiu ir um pouco mais longe e (re) descobrir a vers\303\243o C. Nota : Na se\303\247\303\243o Treinamento (modific\303\241vel), instalei os valores para o primeiro uso.

restart: with(Student[LinearAlgebra]): A := Matrix(3,4, [ 3, 2, 3, 4, 5, 6, 7, 8, -9,10,11,12]); M := A:

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSJBR0YoLUknUlRBQkxFR0YoNiUiNWVwJmVdR2x1WSU9LUknTUFUUklYR0YoNiM3JTcmLUkjbW5HNiRGJi9JK21vZHVsZW5hbWVHRihGJDYjUSIzRigtRjg2I1EiMkYoRjctRjg2I1EiNEYoNyYtRjg2I1EiNUYoLUY4NiNRIjZGKC1GODYjUSI3RigtRjg2I1EiOEYoNyYtRjg2I1ErJnVtaW51czA7OUYoLUY4NiNRIzEwRigtRjg2I1EjMTFGKC1GODYjUSMxMkYoSSdNYXRyaXhHRiU3Iy1GaG42Iy9JJCVpZEdGKEYx

M;

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyMtSSdSVEFCTEVHRig2JSI1ZXAmZV1HbHVZJT0tSSdNQVRSSVhHRig2IzclNyYtSSNtbkc2JEYmL0krbW9kdWxlbmFtZUdGKEYkNiNRIjNGKC1GNjYjUSIyRihGNS1GNjYjUSI0Rig3Ji1GNjYjUSI1RigtRjY2I1EiNkYoLUY2NiNRIjdGKC1GNjYjUSI4Rig3Ji1GNjYjUSsmdW1pbnVzMDs5RigtRjY2I1EjMTBGKC1GNjYjUSMxMUYoLUY2NiNRIzEyRihJJ01hdHJpeEdGJTcjLUZmbjYjL0kkJWlkR0YoRi8=

P := Matrix(3,3, [ 1/3, 0, 0, -5/3, 1, 0, 9/3, 0, 1 ]): M := P.M: igcd(-63, -10, 59, -3);

IiIi

restart: with(Student[LinearAlgebra]): A := RandomMatrix(3, 4); M := A:

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSJBR0YoLUknUlRBQkxFR0YoNiUiNWVwJmVdR2x1WSU9LUknTUFUUklYR0YoNiM3JTcmLUkjbW5HNiRGJi9JK21vZHVsZW5hbWVHRihGJDYjUSwmdW1pbnVzMDszMkYoLUY4NiNRIzI3RigtRjg2I1EjOTlGKC1GODYjUSM5MkYoNyYtRjg2I1EsJnVtaW51czA7NzRGKC1GODYjUSI4RigtRjg2I1EjMjlGKC1GODYjUSwmdW1pbnVzMDszMUYoNyYtRjg2I1ErJnVtaW51czA7NEYoLUY4NiNRIzY5RigtRjg2I1EjNDRGKC1GODYjUSM2N0YoSSdNYXRyaXhHRiU3Iy1GW282Iy9JJCVpZEdGKEYx

M;

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyMtSSdSVEFCTEVHRig2JSI1ZXAmZV1HbHVZJT0tSSdNQVRSSVhHRig2IzclNyYtSSNtbkc2JEYmL0krbW9kdWxlbmFtZUdGKEYkNiNRLCZ1bWludXMwOzMyRigtRjY2I1EjMjdGKC1GNjYjUSM5OUYoLUY2NiNRIzkyRig3Ji1GNjYjUSwmdW1pbnVzMDs3NEYoLUY2NiNRIjhGKC1GNjYjUSMyOUYoLUY2NiNRLCZ1bWludXMwOzMxRig3Ji1GNjYjUSsmdW1pbnVzMDs0RigtRjY2I1EjNjlGKC1GNjYjUSM0NEYoLUY2NiNRIzY3RihJJ01hdHJpeEdGJTcjLUZpbjYjL0kkJWlkR0YoRi8=

P := Matrix(3,3, [ 1, 0, 0, 0, 1, 0, 0, 0, 1 ]): M := P.M: igcd(-63, -10, 59, -3);

IiIi