Resolva um sistema com as matrizes elementares sem introduzir fra\303\247\303\265es.Xhumga bernard Amadora em matem\303\241tica e linguagem C. Iniciante no bordo 15.Maple Cloud : mathc
<Text-field style="Heading 1" layout="Heading 1"><Font encoding="UTF-8"> Introdu\303\247\303\243o</Font></Text-field>Tentei resolver um sistema de equa\303\247\303\265es usando as matrizes elementares sem introduzir as fra\303\247\303\265es. A vers\303\243o A usa duas matrizes P1 e P2. P1 para multiplicar pelo piv\303\264 todas as linhas abaixo ou acima do piv\303\264. P2 para definir para "0" todos os coeficientes abaixo ou acima do piv\303\264. (M: = P2.P1.M;) A vers\303\243o B usa um \303\272nico molde que faz todo o trabalho. (M: = P.M;) Para encontrar essa matriz, simplesmente multipliquei P2 e P1. (P: = P2.P1;)
<Text-field style="Heading 1" layout="Heading 1"><Font encoding="UTF-8">Inicializa\303\247\303\243o</Font></Text-field> restart: with(Student[LinearAlgebra]): randomize(): A := RandomMatrix(3, 4): M := A; LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSJNR0YoLUknUlRBQkxFR0YoNiUiNVk/P0UzZlluVz0tSSdNQVRSSVhHRig2IzclNyYtSSNtbkc2JEYmL0krbW9kdWxlbmFtZUdGKEYkNiNRIzIxRigtRjg2I1EjOTFGKC1GODYjUSI3RigtRjg2I1ErJnVtaW51czA7NkYoNyYtRjg2I1EjNTBGKC1GODYjUSwmdW1pbnVzMDs5NUYoLUY4NiNRIzE0RigtRjg2I1EsJnVtaW51czA7ODNGKDcmLUY4NiNRIzI3RigtRjg2I1EsJnVtaW51czA7OTJGKC1GODYjUSwmdW1pbnVzMDsxOEYoLUY4NiNRIzc4RihJJ01hdHJpeEdGJTcjLUZbbzYjL0kkJWlkR0YoRjE=
<Text-field style="Heading 1" layout="Heading 1"><Font encoding="UTF-8">Exemplo num\303\251rico (fixo)</Font></Text-field> restart: with(Student[LinearAlgebra]): A := Matrix(3,4, [ -2, 31,-91,-50, 66,-53,-96,-29, 57, 74,-23, 58]): M := A; LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSJNR0YoLUknUlRBQkxFR0YoNiUiNVk/P0UzZlluVz0tSSdNQVRSSVhHRig2IzclNyYtSSNtbkc2JEYmL0krbW9kdWxlbmFtZUdGKEYkNiNRKyZ1bWludXMwOzJGKC1GODYjUSMzMUYoLUY4NiNRLCZ1bWludXMwOzkxRigtRjg2I1EsJnVtaW51czA7NTBGKDcmLUY4NiNRIzY2RigtRjg2I1EsJnVtaW51czA7NTNGKC1GODYjUSwmdW1pbnVzMDs5NkYoLUY4NiNRLCZ1bWludXMwOzI5Rig3Ji1GODYjUSM1N0YoLUY4NiNRIzc0RigtRjg2I1EsJnVtaW51czA7MjNGKC1GODYjUSM1OEYoSSdNYXRyaXhHRiU3Iy1GW282Iy9JJCVpZEdGKEYx P := Matrix(3,3, [ -1, 0, 0, 0, 2, 0, 0, 0, 2 ]): M := P.M: P := Matrix(3,3, [ 1, 0, 0, -66, 1, 0, -57, 0, 1 ]): M := P.M; LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSJNR0YoLUknUlRBQkxFR0YoNiUiNWkhKilIJzNmWW5XPS1JJ01BVFJJWEdGKDYjNyU3Ji1JI21uRzYkRiYvSSttb2R1bGVuYW1lR0YoRiQ2I1EiMkYoLUY4NiNRLCZ1bWludXMwOzMxRigtRjg2I1EjOTFGKC1GODYjUSM1MEYoNyYtRjg2I1EiMEYoLUY4NiNRJTE5NDBGKC1GODYjUS4mdW1pbnVzMDs2MTk4RigtRjg2I1EuJnVtaW51czA7MzM1OEYoNyZGSC1GODYjUSUxOTE1RigtRjg2I1EuJnVtaW51czA7NTIzM0YoLUY4NiNRLiZ1bWludXMwOzI3MzRGKEknTWF0cml4R0YlNyMtRmhuNiMvSSQlaWRHRihGMQ== P := Matrix(3,3, [ 1, 0, 0, 0, 1, 0, 0, 0, 1940 ]): M := P.M: P := Matrix(3,3, [ 1, 0, 0, 0, 1, 0, 0, -1915, 1 ]): M := P.M; LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSJNR0YoLUknUlRBQkxFR0YoNiUiNVlPKUgnM2ZZblc9LUknTUFUUklYR0YoNiM3JTcmLUkjbW5HNiRGJi9JK21vZHVsZW5hbWVHRihGJDYjUSIyRigtRjg2I1EsJnVtaW51czA7MzFGKC1GODYjUSM5MUYoLUY4NiNRIzUwRig3Ji1GODYjUSIwRigtRjg2I1ElMTk0MEYoLUY4NiNRLiZ1bWludXMwOzYxOThGKC1GODYjUS4mdW1pbnVzMDszMzU4Rig3JkZIRkgtRjg2I1EoMTcxNzE1MEYoLUY4NiNRKDExMjY2MTBGKEknTWF0cml4R0YlNyMtRmVuNiMvSSQlaWRHRihGMQ== P := Matrix(3,3, [ 1717150, 0, 0, 0, 1717150, 0, 0, 0, 1 ]): M := P.M: P := Matrix(3,3, [ 1, 0, -91, 0, 1, 6198, 0, 0, 1 ]): M := P.M; LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSJNR0YoLUknUlRBQkxFR0YoNiUiNTFrKUgnM2ZZblc9LUknTUFUUklYR0YoNiM3JTcmLUkjbW5HNiRGJi9JK21vZHVsZW5hbWVHRihGJDYjUSgzNDM0MzAwRigtRjg2I1EyJnVtaW51czA7NTMyMzE2NTBGKC1GODYjUSIwRigtRjg2I1EyJnVtaW51czA7MTY2NjQwMTBGKDcmRkEtRjg2I1ErMzMzMTI3MTAwMEYoRkEtRjg2I1ErMTIxNjUzOTA4MEYoNyZGQUZBLUY4NiNRKDE3MTcxNTBGKC1GODYjUSgxMTI2NjEwRihJJ01hdHJpeEdGJTcjLUZVNiMvSSQlaWRHRihGMQ== P := Matrix(3,3, [ 3331271000, 0, 0, 0, 1, 0, 0, 0, 1 ]): M := P.M: P := Matrix(3,3, [ 1, 53231650, 0, 0, 1, 0, 0, 0, 1 ]): M := P.M; LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSJNR0YoLUknUlRBQkxFR0YoNiUiNSEqNClIJzNmWW5XPS1JJ01BVFJJWEdGKDYjNyU3Ji1JI21uRzYkRiYvSSttb2R1bGVuYW1lR0YoRiQ2I1EyMTE0NDA1ODM5OTUzMDAwMDBGKC1GODYjUSIwRihGPi1GODYjUTE5MjQ2MDQ5MjYxMTcyMDAwRig3JkY+LUY4NiNRKzMzMzEyNzEwMDBGKEY+LUY4NiNRKzEyMTY1MzkwODBGKDcmRj5GPi1GODYjUSgxNzE3MTUwRigtRjg2I1EoMTEyNjYxMEYoSSdNYXRyaXhHRiU3Iy1GUjYjL0kkJWlkR0YoRjE= P := ZeroMatrix(3): P[1,1] := 1/(igcd(11440583995300000, 9246049261172000)): P[2,2] := 1/(igcd( 3331271000, 1216539080)): P[3,3] := 1/(igcd( 1717150, 1126610)): M := P.M; LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSJNR0YoLUknUlRBQkxFR0YoNiUiNU1gKEgnM2ZZblc9LUknTUFUUklYR0YoNiM3JTcmLUkjbW5HNiRGJi9JK21vZHVsZW5hbWVHRihGJDYjUSc4NTg1NzVGKC1GODYjUSIwRihGPi1GODYjUSc2OTM4ODNGKDcmRj5GN0Y+LUY4NiNRJzMxMzU0MUYoNyZGPkY+LUY4NiNRJzE3MTcxNUYoLUY4NiNRJzExMjY2MUYoSSdNYXRyaXhHRiU3Iy1GTzYjL0kkJWlkR0YoRjE= ReducedRowEchelonForm(A); LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyMtSSdSVEFCTEVHRig2JSI1TSR5SCczZlluVz0tSSdNQVRSSVhHRig2IzclNyYtSSNtbkc2JEYmL0krbW9kdWxlbmFtZUdGKEYkNiNRIjFGKC1GNjYjUSIwRihGPC1JJm1mcmFjR0Y3NiQtRjY2I1EnNjkzODgzRigtRjY2I1EnODU4NTc1Rig3JkY8RjVGPC1GQDYkLUY2NiNRJzMxMzU0MUYoRkU3JkY8RjxGNS1GQDYkLUY2NiNRJzExMjY2MUYoLUY2NiNRJzE3MTcxNUYoSSdNYXRyaXhHRiU3Iy1GVzYjL0kkJWlkR0YoRi8=
<Text-field style="Heading 1" layout="Heading 1"><Font encoding="UTF-8">A) Exemplo num\303\251rico (modific\303\241vel)</Font></Text-field> restart: with(Student[LinearAlgebra]): A := Matrix(3,4, [-54, 31,-91,-50, 66,-53,-96,-29, 57, 74,-23, 58]): M := A; LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSJNR0YoLUknUlRBQkxFR0YoNiUiNVk/P0UzZlluVz0tSSdNQVRSSVhHRig2IzclNyYtSSNtbkc2JEYmL0krbW9kdWxlbmFtZUdGKEYkNiNRLCZ1bWludXMwOzU0RigtRjg2I1EjMzFGKC1GODYjUSwmdW1pbnVzMDs5MUYoLUY4NiNRLCZ1bWludXMwOzUwRig3Ji1GODYjUSM2NkYoLUY4NiNRLCZ1bWludXMwOzUzRigtRjg2I1EsJnVtaW51czA7OTZGKC1GODYjUSwmdW1pbnVzMDsyOUYoNyYtRjg2I1EjNTdGKC1GODYjUSM3NEYoLUY4NiNRLCZ1bWludXMwOzIzRigtRjg2I1EjNThGKEknTWF0cml4R0YlNyMtRltvNiMvSSQlaWRHRihGMQ== P1 := Matrix(3,3, [ 1, 0, 0, 0, M[1,1], 0, 0, 0, M[1,1] ]): P2 := Matrix(3,3, [ 1, 0, 0, -M[2,1], 1, 0, -M[3,1], 0, 1 ]): M := P2.P1.M; LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSJNR0YoLUknUlRBQkxFR0YoNiUiNWkhKilIJzNmWW5XPS1JJ01BVFJJWEdGKDYjNyU3Ji1JI21uRzYkRiYvSSttb2R1bGVuYW1lR0YoRiQ2I1EsJnVtaW51czA7NTRGKC1GODYjUSMzMUYoLUY4NiNRLCZ1bWludXMwOzkxRigtRjg2I1EsJnVtaW51czA7NTBGKDcmLUY4NiNRIjBGKC1GODYjUSQ4MTZGKC1GODYjUSYxMTE5MEYoLUY4NiNRJTQ4NjZGKDcmRkgtRjg2I1EuJnVtaW51czA7NTc2M0YoLUY4NiNRJTY0MjlGKC1GODYjUS0mdW1pbnVzMDsyODJGKEknTWF0cml4R0YlNyMtRmhuNiMvSSQlaWRHRihGMQ== P1 := Matrix(3,3, [ 1, 0, 0, 0, 1, 0, 0, 0, M[2,2] ]): P2 := Matrix(3,3, [ 1, 0, 0, 0, 1, 0, 0, -M[3,2], 1 ]): M := P2.P1.M; LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSJNR0YoLUknUlRBQkxFR0YoNiUiNVlPKUgnM2ZZblc9LUknTUFUUklYR0YoNiM3JTcmLUkjbW5HNiRGJi9JK21vZHVsZW5hbWVHRihGJDYjUSwmdW1pbnVzMDs1NEYoLUY4NiNRIzMxRigtRjg2I1EsJnVtaW51czA7OTFGKC1GODYjUSwmdW1pbnVzMDs1MEYoNyYtRjg2I1EiMEYoLUY4NiNRJDgxNkYoLUY4NiNRJjExMTkwRigtRjg2I1ElNDg2NkYoNyZGSEZILUY4NiNRKTY5NzM0MDM0RigtRjg2I1EpMjc4MTI2NDZGKEknTWF0cml4R0YlNyMtRmVuNiMvSSQlaWRHRihGMQ== P1 := Matrix(3,3, [ M[3,3], 0, 0, 0, M[3,3], 0, 0, 0, 1 ]): P2 := Matrix(3,3, [ 1, 0, -M[1,3], 0, 1, -M[2,3], 0, 0, 1 ]): M := P2.P1.M; LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSJNR0YoLUknUlRBQkxFR0YoNiUiNTFrKUgnM2ZZblc9LUknTUFUUklYR0YoNiM3JTcmLUkjbW5HNiRGJi9JK21vZHVsZW5hbWVHRihGJDYjUTQmdW1pbnVzMDszNzY1NjM3ODM2RigtRjg2I1ErMjE2MTc1NTA1NEYoLUY4NiNRIjBGKC1GODYjUTMmdW1pbnVzMDs5NTU3NTA5MTRGKDcmRkEtRjg2I1EsNTY5MDI5NzE3NDRGKEZBLUY4NiNRLDI4MTAyMzAwNzA0Rig3JkZBRkEtRjg2I1EpNjk3MzQwMzRGKC1GODYjUSkyNzgxMjY0NkYoSSdNYXRyaXhHRiU3Iy1GVTYjL0kkJWlkR0YoRjE= P1 := Matrix(3,3, [ M[2,2], 0, 0, 0, 1, 0, 0, 0, 1 ]): P2 := Matrix(3,3, [ 1, -M[1,2], 0, 0, 1, 0, 0, 0, 1 ]): M := P2.P1.M; LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSJNR0YoLUknUlRBQkxFR0YoNiUiNSEqNClIJzNmWW5XPS1JJ01BVFJJWEdGKDYjNyU3Ji1JI21uRzYkRiYvSSttb2R1bGVuYW1lR0YoRiQ2I1E/JnVtaW51czA7MjE0Mjc1OTgzMzgwMDQ1MzA1OTg0RigtRjg2I1EiMEYoRj4tRjg2I1E/JnVtaW51czA7MTE1MTM1MzU3ODI5NTQzOTMyMDMyRig3JkY+LUY4NiNRLDU2OTAyOTcxNzQ0RihGPi1GODYjUSwyODEwMjMwMDcwNEYoNyZGPkY+LUY4NiNRKTY5NzM0MDM0RigtRjg2I1EpMjc4MTI2NDZGKEknTWF0cml4R0YlNyMtRlI2Iy9JJCVpZEdGKEYx P := ZeroMatrix(3): P[1,1] := 1/(igcd(M[1,1], M[1,4])): P[2,2] := 1/(igcd(M[2,2], M[2,4])): P[3,3] := 1/(igcd(M[3,3], M[3,4])): M := P.M; LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSJNR0YoLUknUlRBQkxFR0YoNiUiNU1gKEgnM2ZZblc9LUknTUFUUklYR0YoNiM3JTcmLUkjbW5HNiRGJi9JK21vZHVsZW5hbWVHRihGJDYjUTEmdW1pbnVzMDsxMjkxMzcxRigtRjg2I1EiMEYoRj4tRjg2I1EwJnVtaW51czA7NjkzODgzRig3JkY+LUY4NiNRJzQzMDQ1N0YoRj4tRjg2I1EnMjEyNTg3Rig3JkY+Rj4tRjg2I1EmMjUzMjFGKC1GODYjUSYxMDA5OUYoSSdNYXRyaXhHRiU3Iy1GUjYjL0kkJWlkR0YoRjE= ReducedRowEchelonForm(A); LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyMtSSdSVEFCTEVHRig2JSI1TSR5SCczZlluVz0tSSdNQVRSSVhHRig2IzclNyYtSSNtbkc2JEYmL0krbW9kdWxlbmFtZUdGKEYkNiNRIjFGKC1GNjYjUSIwRihGPC1JJm1mcmFjR0Y3NiQtRjY2I1EnNjkzODgzRigtRjY2I1EoMTI5MTM3MUYoNyZGPEY1RjwtRkA2JC1GNjYjUScyMTI1ODdGKC1GNjYjUSc0MzA0NTdGKDcmRjxGPEY1LUZANiQtRjY2I1EmMTAwOTlGKC1GNjYjUSYyNTMyMUYoSSdNYXRyaXhHRiU3Iy1GWjYjL0kkJWlkR0YoRi8=
<Text-field style="Heading 1" layout="Heading 1"><Font encoding="UTF-8">Exemplo num\303\251rico (aleat\303\263rio)</Font></Text-field> restart: with(Student[LinearAlgebra]): randomize(): A := RandomMatrix(3, 4): M := A; LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSJNR0YoLUknUlRBQkxFR0YoNiUiNVk/P0UzZlluVz0tSSdNQVRSSVhHRig2IzclNyYtSSNtbkc2JEYmL0krbW9kdWxlbmFtZUdGKEYkNiNRIzMxRigtRjg2I1EsJnVtaW51czA7NTJGKC1GODYjUSM3MkYoLUY4NiNRLCZ1bWludXMwOzYyRig3Ji1GODYjUSwmdW1pbnVzMDsxNkYoRkEtRjg2I1EsJnVtaW51czA7NjdGKC1GODYjUSMxMUYoNyYtRjg2I1EjMzVGKC1GODYjUSM1N0YoLUY4NiNRIzYyRigtRjg2I1EjNTBGKEknTWF0cml4R0YlNyMtRmhuNiMvSSQlaWRHRihGMQ== P1 := Matrix(3,3, [ 1, 0, 0, 0, M[1,1], 0, 0, 0, M[1,1] ]): P2 := Matrix(3,3, [ 1, 0, 0, -M[2,1], 1, 0, -M[3,1], 0, 1 ]): M := P2.P1.M; LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSJNR0YoLUknUlRBQkxFR0YoNiUiNT08JEgnM2ZZblc9LUknTUFUUklYR0YoNiM3JTcmLUkjbW5HNiRGJi9JK21vZHVsZW5hbWVHRihGJDYjUSMzMUYoLUY4NiNRLCZ1bWludXMwOzUyRigtRjg2I1EjNzJGKC1GODYjUSwmdW1pbnVzMDs2MkYoNyYtRjg2I1EiMEYoLUY4NiNRJTE0MDBGKC1GODYjUS0mdW1pbnVzMDs5MjVGKC1GODYjUS0mdW1pbnVzMDs2NTFGKDcmRkgtRjg2I1ElMzU4N0YoLUY4NiNRLSZ1bWludXMwOzU5OEYoLUY4NiNRJTM3MjBGKEknTWF0cml4R0YlNyMtRmhuNiMvSSQlaWRHRihGMQ== P1 := Matrix(3,3, [ 1, 0, 0, 0, 1, 0, 0, 0, M[2,2] ]): P2 := Matrix(3,3, [ 1, 0, 0, 0, 1, 0, 0, -M[3,2], 1 ]): M := P2.P1.M; LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSJNR0YoLUknUlRBQkxFR0YoNiUiNS1qI0gnM2ZZblc9LUknTUFUUklYR0YoNiM3JTcmLUkjbW5HNiRGJi9JK21vZHVsZW5hbWVHRihGJDYjUSMzMUYoLUY4NiNRLCZ1bWludXMwOzUyRigtRjg2I1EjNzJGKC1GODYjUSwmdW1pbnVzMDs2MkYoNyYtRjg2I1EiMEYoLUY4NiNRJTE0MDBGKC1GODYjUS0mdW1pbnVzMDs5MjVGKC1GODYjUS0mdW1pbnVzMDs2NTFGKDcmRkhGSC1GODYjUSgyNDgwNzc1RigtRjg2I1EoNzU0MzEzN0YoSSdNYXRyaXhHRiU3Iy1GZW42Iy9JJCVpZEdGKEYx P1 := Matrix(3,3, [ M[3,3], 0, 0, 0, M[3,3], 0, 0, 0, 1 ]): P2 := Matrix(3,3, [ 1, 0, -M[1,3], 0, 1, -M[2,3], 0, 0, 1 ]): M := P2.P1.M; LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSJNR0YoLUknUlRBQkxFR0YoNiUiNWkhSEgnM2ZZblc9LUknTUFUUklYR0YoNiM3JTcmLUkjbW5HNiRGJi9JK21vZHVsZW5hbWVHRihGJDYjUSk3NjkwNDAyNUYoLUY4NiNRMyZ1bWludXMwOzEyOTAwMDMwMEYoLUY4NiNRIjBGKC1GODYjUTMmdW1pbnVzMDs2OTY5MTM5MTRGKDcmRkEtRjg2I1ErMzQ3MzA4NTAwMEYoRkEtRjg2I1ErNTM2MjQxNzIwMEYoNyZGQUZBLUY4NiNRKDI0ODA3NzVGKC1GODYjUSg3NTQzMTM3RihJJ01hdHJpeEdGJTcjLUZVNiMvSSQlaWRHRihGMQ== P1 := Matrix(3,3, [ M[2,2], 0, 0, 0, 1, 0, 0, 0, 1 ]): P2 := Matrix(3,3, [ 1, -M[1,2], 0, 0, 1, 0, 0, 0, 1 ]): M := P2.P1.M; LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSJNR0YoLUknUlRBQkxFR0YoNiUiNVlPI0gnM2ZZblc9LUknTUFUUklYR0YoNiM3JTcmLUkjbW5HNiRGJi9JK21vZHVsZW5hbWVHRihGJDYjUTMyNjcwOTQyMTU2NjcxMjUwMDBGKC1GODYjUSIwRihGPi1GODYjUT0mdW1pbnVzMDsxNzI4Njg3ODMzNDc5NTMwMDAwRig3JkY+LUY4NiNRKzM0NzMwODUwMDBGKEY+LUY4NiNRKzUzNjI0MTcyMDBGKDcmRj5GPi1GODYjUSgyNDgwNzc1RigtRjg2I1EoNzU0MzEzN0YoSSdNYXRyaXhHRiU3Iy1GUjYjL0kkJWlkR0YoRjE= P := ZeroMatrix(3): P[1,1] := 1/(igcd(M[1,1], M[1,4])): P[2,2] := 1/(igcd(M[2,2], M[2,4])): P[3,3] := 1/(igcd(M[3,3], M[3,4])): M := P.M; LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSJNR0YoLUknUlRBQkxFR0YoNiUiNSEqeiJIJzNmWW5XPS1JJ01BVFJJWEdGKDYjNyU3Ji1JI21uRzYkRiYvSSttb2R1bGVuYW1lR0YoRiQ2I1EmMjY2NzVGKC1GODYjUSIwRihGPi1GODYjUTAmdW1pbnVzMDsxNzI2NDZGKDcmRj5GN0Y+LUY4NiNRJjQxMTg2Rig3JkY+Rj5GNy1GODYjUSY4MTEwOUYoSSdNYXRyaXhHRiU3Iy1GTDYjL0kkJWlkR0YoRjE= ReducedRowEchelonForm(A); LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyMtSSdSVEFCTEVHRig2JSI1ISo0I0gnM2ZZblc9LUknTUFUUklYR0YoNiM3JTcmLUkjbW5HNiRGJi9JK21vZHVsZW5hbWVHRihGJDYjUSIxRigtRjY2I1EiMEYoRjwtSSVtcm93R0Y3NiQtSSNtb0dGNzYjUSomdW1pbnVzMDtGKC1JJm1mcmFjR0Y3NiQtRjY2I1EnMTcyNjQ2RigtRjY2I1EmMjY2NzVGKDcmRjxGNUY8LUZHNiQtRjY2I1EmNDExODZGKEZMNyZGPEY8RjUtRkc2JC1GNjYjUSY4MTEwOUYoRkxJJ01hdHJpeEdGJTcjLUZlbjYjL0kkJWlkR0YoRi8=
<Text-field style="Heading 1" layout="Heading 1"><Font encoding="UTF-8">B) Exemplo num\303\251rico (modific\303\241vel)</Font></Text-field> restart: with(Student[LinearAlgebra]): A := Matrix(3,4, [-54, 31,-91,-50, 66,-53,-96,-29, 57, 74,-23, 58]): M := A; LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSJNR0YoLUknUlRBQkxFR0YoNiUiNVk/P0UzZlluVz0tSSdNQVRSSVhHRig2IzclNyYtSSNtbkc2JEYmL0krbW9kdWxlbmFtZUdGKEYkNiNRLCZ1bWludXMwOzU0RigtRjg2I1EjMzFGKC1GODYjUSwmdW1pbnVzMDs5MUYoLUY4NiNRLCZ1bWludXMwOzUwRig3Ji1GODYjUSM2NkYoLUY4NiNRLCZ1bWludXMwOzUzRigtRjg2I1EsJnVtaW51czA7OTZGKC1GODYjUSwmdW1pbnVzMDsyOUYoNyYtRjg2I1EjNTdGKC1GODYjUSM3NEYoLUY4NiNRLCZ1bWludXMwOzIzRigtRjg2I1EjNThGKEknTWF0cml4R0YlNyMtRltvNiMvSSQlaWRHRihGMQ== P := Matrix(3,3, [ 1, 0, 0, -M[2,1], M[1,1], 0, -M[3,1], 0, M[1,1] ]): M := P.M; LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSJNR0YoLUknUlRBQkxFR0YoNiUiNUEpKSlIJzNmWW5XPS1JJ01BVFJJWEdGKDYjNyU3Ji1JI21uRzYkRiYvSSttb2R1bGVuYW1lR0YoRiQ2I1EsJnVtaW51czA7NTRGKC1GODYjUSMzMUYoLUY4NiNRLCZ1bWludXMwOzkxRigtRjg2I1EsJnVtaW51czA7NTBGKDcmLUY4NiNRIjBGKC1GODYjUSQ4MTZGKC1GODYjUSYxMTE5MEYoLUY4NiNRJTQ4NjZGKDcmRkgtRjg2I1EuJnVtaW51czA7NTc2M0YoLUY4NiNRJTY0MjlGKC1GODYjUS0mdW1pbnVzMDsyODJGKEknTWF0cml4R0YlNyMtRmhuNiMvSSQlaWRHRihGMQ== P := Matrix(3,3, [ 1, 0, 0, 0, 1, 0, 0, -M[3,2], M[2,2] ]): M := P.M; LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSJNR0YoLUknUlRBQkxFR0YoNiUiNW1KKUgnM2ZZblc9LUknTUFUUklYR0YoNiM3JTcmLUkjbW5HNiRGJi9JK21vZHVsZW5hbWVHRihGJDYjUSwmdW1pbnVzMDs1NEYoLUY4NiNRIzMxRigtRjg2I1EsJnVtaW51czA7OTFGKC1GODYjUSwmdW1pbnVzMDs1MEYoNyYtRjg2I1EiMEYoLUY4NiNRJDgxNkYoLUY4NiNRJjExMTkwRigtRjg2I1ElNDg2NkYoNyZGSEZILUY4NiNRKTY5NzM0MDM0RigtRjg2I1EpMjc4MTI2NDZGKEknTWF0cml4R0YlNyMtRmVuNiMvSSQlaWRHRihGMQ== P := Matrix(3,3, [ M[3,3], 0, -M[1,3], 0, M[3,3], -M[2,3], 0, 0, 1 ]): M := P.M; LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSJNR0YoLUknUlRBQkxFR0YoNiUiNSdvJilIJzNmWW5XPS1JJ01BVFJJWEdGKDYjNyU3Ji1JI21uRzYkRiYvSSttb2R1bGVuYW1lR0YoRiQ2I1E0JnVtaW51czA7Mzc2NTYzNzgzNkYoLUY4NiNRKzIxNjE3NTUwNTRGKC1GODYjUSIwRigtRjg2I1EzJnVtaW51czA7OTU1NzUwOTE0Rig3JkZBLUY4NiNRLDU2OTAyOTcxNzQ0RihGQS1GODYjUSwyODEwMjMwMDcwNEYoNyZGQUZBLUY4NiNRKTY5NzM0MDM0RigtRjg2I1EpMjc4MTI2NDZGKEknTWF0cml4R0YlNyMtRlU2Iy9JJCVpZEdGKEYx P := Matrix(3,3, [ M[2,2], -M[1,2], 0, 0, 1, 0, 0, 0, 1 ]): M := P.M; LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSJNR0YoLUknUlRBQkxFR0YoNiUiNUkrKUgnM2ZZblc9LUknTUFUUklYR0YoNiM3JTcmLUkjbW5HNiRGJi9JK21vZHVsZW5hbWVHRihGJDYjUT8mdW1pbnVzMDsyMTQyNzU5ODMzODAwNDUzMDU5ODRGKC1GODYjUSIwRihGPi1GODYjUT8mdW1pbnVzMDsxMTUxMzUzNTc4Mjk1NDM5MzIwMzJGKDcmRj4tRjg2I1EsNTY5MDI5NzE3NDRGKEY+LUY4NiNRLDI4MTAyMzAwNzA0Rig3JkY+Rj4tRjg2I1EpNjk3MzQwMzRGKC1GODYjUSkyNzgxMjY0NkYoSSdNYXRyaXhHRiU3Iy1GUjYjL0kkJWlkR0YoRjE= P := ZeroMatrix(3): P[1,1] := 1/(igcd(M[1,1], M[1,4])): P[2,2] := 1/(igcd(M[2,2], M[2,4])): P[3,3] := 1/(igcd(M[3,3], M[3,4])): M := P.M; LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSJNR0YoLUknUlRBQkxFR0YoNiUiNV1EKUgnM2ZZblc9LUknTUFUUklYR0YoNiM3JTcmLUkjbW5HNiRGJi9JK21vZHVsZW5hbWVHRihGJDYjUTEmdW1pbnVzMDsxMjkxMzcxRigtRjg2I1EiMEYoRj4tRjg2I1EwJnVtaW51czA7NjkzODgzRig3JkY+LUY4NiNRJzQzMDQ1N0YoRj4tRjg2I1EnMjEyNTg3Rig3JkY+Rj4tRjg2I1EmMjUzMjFGKC1GODYjUSYxMDA5OUYoSSdNYXRyaXhHRiU3Iy1GUjYjL0kkJWlkR0YoRjE= ReducedRowEchelonForm(A); LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyMtSSdSVEFCTEVHRig2JSI1dXQoSCczZlluVz0tSSdNQVRSSVhHRig2IzclNyYtSSNtbkc2JEYmL0krbW9kdWxlbmFtZUdGKEYkNiNRIjFGKC1GNjYjUSIwRihGPC1JJm1mcmFjR0Y3NiQtRjY2I1EnNjkzODgzRigtRjY2I1EoMTI5MTM3MUYoNyZGPEY1RjwtRkA2JC1GNjYjUScyMTI1ODdGKC1GNjYjUSc0MzA0NTdGKDcmRjxGPEY1LUZANiQtRjY2I1EmMTAwOTlGKC1GNjYjUSYyNTMyMUYoSSdNYXRyaXhHRiU3Iy1GWjYjL0kkJWlkR0YoRi8=
<Text-field style="Heading 1" layout="Heading 1"><Font encoding="UTF-8"> Exemplo num\303\251rico (aleat\303\263rio) </Font></Text-field> restart: with(Student[LinearAlgebra]): randomize(): A := RandomMatrix(3, 4): M := A; LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSJNR0YoLUknUlRBQkxFR0YoNiUiNVk/P0UzZlluVz0tSSdNQVRSSVhHRig2IzclNyYtSSNtbkc2JEYmL0krbW9kdWxlbmFtZUdGKEYkNiNRIjRGKC1GODYjUSsmdW1pbnVzMDszRigtRjg2I1EjNzVGKC1GODYjUSMyM0YoNyYtRjg2I1EsJnVtaW51czA7ODZGKC1GODYjUSM1NUYoLUY4NiNRLCZ1bWludXMwOzYwRigtRjg2I1EsJnVtaW51czA7NzZGKDcmLUY4NiNRLCZ1bWludXMwOzM0RigtRjg2I1EjODFGKC1GODYjUSMzMkYoLUY4NiNRLCZ1bWludXMwOzg0RihJJ01hdHJpeEdGJTcjLUZbbzYjL0kkJWlkR0YoRjE= P := Matrix(3,3, [ 1, 0, 0, -M[2,1], M[1,1], 0, -M[3,1], 0, M[1,1] ]): M := P.M; LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSJNR0YoLUknUlRBQkxFR0YoNiUiNXk5JEgnM2ZZblc9LUknTUFUUklYR0YoNiM3JTcmLUkjbW5HNiRGJi9JK21vZHVsZW5hbWVHRihGJDYjUSI0RigtRjg2I1ErJnVtaW51czA7M0YoLUY4NiNRIzc1RigtRjg2I1EjMjNGKDcmLUY4NiNRIjBGKC1GODYjUSwmdW1pbnVzMDszOEYoLUY4NiNRJTYyMTBGKC1GODYjUSUxNjc0Rig3JkZILUY4NiNRJDIyMkYoLUY4NiNRJTI2NzhGKC1GODYjUSQ0NDZGKEknTWF0cml4R0YlNyMtRmhuNiMvSSQlaWRHRihGMQ== P := Matrix(3,3, [ 1, 0, 0, 0, 1, 0, 0, -M[3,2], M[2,2] ]): M := P.M; LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSJNR0YoLUknUlRBQkxFR0YoNiUiNUFlI0gnM2ZZblc9LUknTUFUUklYR0YoNiM3JTcmLUkjbW5HNiRGJi9JK21vZHVsZW5hbWVHRihGJDYjUSI0RigtRjg2I1ErJnVtaW51czA7M0YoLUY4NiNRIzc1RigtRjg2I1EjMjNGKDcmLUY4NiNRIjBGKC1GODYjUSwmdW1pbnVzMDszOEYoLUY4NiNRJTYyMTBGKC1GODYjUSUxNjc0Rig3JkZIRkgtRjg2I1ExJnVtaW51czA7MTQ4MDM4NEYoLUY4NiNRMCZ1bWludXMwOzM4ODU3NkYoSSdNYXRyaXhHRiU3Iy1GZW42Iy9JJCVpZEdGKEYx P := Matrix(3,3, [ M[3,3], 0, -M[1,3], 0, M[3,3], -M[2,3], 0, 0, 1 ]): M := P.M; LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSJNR0YoLUknUlRBQkxFR0YoNiUiNVUkR0gnM2ZZblc9LUknTUFUUklYR0YoNiM3JTcmLUkjbW5HNiRGJi9JK21vZHVsZW5hbWVHRihGJDYjUTEmdW1pbnVzMDs1OTIxNTM2RigtRjg2I1EoNDQ0MTE1MkYoLUY4NiNRIjBGKC1GODYjUTEmdW1pbnVzMDs0OTA1NjMyRig3JkZBLUY4NiNRKTU2MjU0NTkyRihGQS1GODYjUTImdW1pbnVzMDs2NTEwNTg1NkYoNyZGQUZBLUY4NiNRMSZ1bWludXMwOzE0ODAzODRGKC1GODYjUTAmdW1pbnVzMDszODg1NzZGKEknTWF0cml4R0YlNyMtRlU2Iy9JJCVpZEdGKEYx P := Matrix(3,3, [ M[2,2], -M[1,2], 0, 0, 1, 0, 0, 0, 1 ]): M := P.M; LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSJNR0YoLUknUlRBQkxFR0YoNiUiNSdvQUgnM2ZZblc9LUknTUFUUklYR0YoNiM3JTcmLUkjbW5HNiRGJi9JK21vZHVsZW5hbWVHRihGJDYjUTkmdW1pbnVzMDszMzMxMTM1OTE2OTMzMTJGKC1GODYjUSIwRihGPi1GODYjUS8xMzE4MDY3NTkyMzk2OEYoNyZGPi1GODYjUSk1NjI1NDU5MkYoRj4tRjg2I1EyJnVtaW51czA7NjUxMDU4NTZGKDcmRj5GPi1GODYjUTEmdW1pbnVzMDsxNDgwMzg0RigtRjg2I1EwJnVtaW51czA7Mzg4NTc2RihJJ01hdHJpeEdGJTcjLUZSNiMvSSQlaWRHRihGMQ== P := ZeroMatrix(3): P[1,1] := 1/(igcd(M[1,1], M[1,4])): P[2,2] := 1/(igcd(M[2,2], M[2,4])): P[3,3] := 1/(igcd(M[3,3], M[3,4])): M := P.M; LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSJNR0YoLUknUlRBQkxFR0YoNiUiNTFfI0gnM2ZZblc9LUknTUFUUklYR0YoNiM3JTcmLUkjbW5HNiRGJi9JK21vZHVsZW5hbWVHRihGJDYjUS8mdW1pbnVzMDs5MjUyNEYoLUY4NiNRIjBGKEY+LUY4NiNRJTM2NjFGKDcmRj4tRjg2I1EmNDYyNjJGKEY+LUY4NiNRLyZ1bWludXMwOzUzNTQxRig3JkY+Rj4tRjg2I1EvJnVtaW51czA7NDYyNjJGKC1GODYjUS8mdW1pbnVzMDsxMjE0M0YoSSdNYXRyaXhHRiU3Iy1GUjYjL0kkJWlkR0YoRjE= ReducedRowEchelonForm(A); LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyMtSSdSVEFCTEVHRig2JSI1SSsjSCczZlluVz0tSSdNQVRSSVhHRig2IzclNyYtSSNtbkc2JEYmL0krbW9kdWxlbmFtZUdGKEYkNiNRIjFGKC1GNjYjUSIwRihGPC1JJW1yb3dHRjc2JC1JI21vR0Y3NiNRKiZ1bWludXMwO0YoLUkmbWZyYWNHRjc2JC1GNjYjUSUzNjYxRigtRjY2I1EmOTI1MjRGKDcmRjxGNUY8LUZANiRGQi1GRzYkLUY2NiNRJjUzNTQxRigtRjY2I1EmNDYyNjJGKDcmRjxGPEY1LUZHNiQtRjY2I1EmMTIxNDNGKEZXSSdNYXRyaXhHRiU3Iy1Gam42Iy9JJCVpZEdGKEYv
<Text-field style="Heading 1" layout="Heading 1"><Font encoding="UTF-8">B') Exemplo num\303\251rico (modific\303\241vel) (matrizes 4x5)</Font></Text-field> restart: with(Student[LinearAlgebra]): A := Matrix(4,5, [-54, 31,-91,-50,-51, 66,-53, 96,-29, 52, 57, 74,-23, 58,-53, 87, 71, 53, 38, 54]): M := A; 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 P := Matrix(4,4, [ 1, 0, 0, 0, -M[2,1], M[1,1], 0, 0, -M[3,1], 0, M[1,1], 0, -M[4,1], 0, 0, M[1,1] ]): M := P.M; 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 P := Matrix(4,4, [ 1, 0, 0, 0, 0, 1, 0, 0, 0, -M[3,2], M[2,2], 0, 0, -M[4,2], 0, M[2,2]] ): M := P.M; 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 P := Matrix(4,4, [ 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, -M[4,3], M[3,3]] ): M := P.M; 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 P := Matrix(4,4, [ M[4,4], 0, 0, -M[1,4], 0, M[4,4], 0, -M[2,4], 0, 0, M[4,4], -M[3,4], 0, 0, 0, 1] ): M := P.M: P := Matrix(4,4, [ M[3,3], 0, -M[1,3], 0, 0, M[3,3], -M[2,3], 0, 0, 0, 1, 0, 0, 0, 0, 1] ): M := P.M: P := Matrix(4,4, [ M[2,2],-M[1,2], 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1] ): M := P.M: P := ZeroMatrix(4): P[1,1] := 1/(igcd(M[1,1], M[1,5])): P[2,2] := 1/(igcd(M[2,2], M[2,5])): P[3,3] := 1/(igcd(M[3,3], M[3,5])): P[4,4] := 1/(igcd(M[4,4], M[4,5])): M := P.M; LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSJNR0YoLUknUlRBQkxFR0YoNiUiNTlrKEgnM2ZZblc9LUknTUFUUklYR0YoNiM3JjcnLUkjbW5HNiRGJi9JK21vZHVsZW5hbWVHRihGJDYjUTImdW1pbnVzMDszMDIzODM4M0YoLUY4NiNRIjBGKEY+Rj4tRjg2I1EpMzU2Mzg0MjlGKDcnRj4tRjg2I1EpMTAwNzk0NjFGKEY+Rj4tRjg2I1EpMTA1MjkzNTNGKDcnRj5GPkZFRj4tRjg2I1EpMTgzMjA3ODZGKDcnRj5GPkY+RkUtRjg2I1ExJnVtaW51czA7MzcwNDc0N0YoSSdNYXRyaXhHRiU3Iy1GUzYjL0kkJWlkR0YoRjE= ReducedRowEchelonForm(A); 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
<Text-field style="Heading 1" layout="Heading 1"><Font encoding="UTF-8"> Exemplo num\303\251rico (aleat\303\263rio) </Font></Text-field> restart: with(Student[LinearAlgebra]): randomize(): A := RandomMatrix(4, 5): M := A; 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 P := Matrix(4,4, [ 1, 0, 0, 0, -M[2,1], M[1,1], 0, 0, -M[3,1], 0, M[1,1], 0, -M[4,1], 0, 0, M[1,1] ]): M := P.M; 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 P := Matrix(4,4, [ 1, 0, 0, 0, 0, 1, 0, 0, 0, -M[3,2], M[2,2], 0, 0, -M[4,2], 0, M[2,2]] ): M := P.M; LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSJNR0YoLUknUlRBQkxFR0YoNiUiNVV4I0gnM2ZZblc9LUknTUFUUklYR0YoNiM3JjcnLUkjbW5HNiRGJi9JK21vZHVsZW5hbWVHRihGJDYjUSMxN0YoLUY4NiNRIzc5RigtRjg2I1EsJnVtaW51czA7OTBGKC1GODYjUSMxNUYoLUY4NiNRLCZ1bWludXMwOzUwRig3Jy1GODYjUSIwRigtRjg2I1ElMjYzNEYoLUY4NiNRLiZ1bWludXMwOzE0MjZGKC1GODYjUSUxNzc5RigtRjg2I1EuJnVtaW51czA7MTAwMEYoNydGS0ZLLUY4NiNRKDE5MTQzMDJGKC1GODYjUTEmdW1pbnVzMDsyMTMwNjI3RigtRjg2I1ExJnVtaW51czA7MTEzNjMxNEYoNydGS0ZLLUY4NiNRMiZ1bWludXMwOzEzODM0MDIyRigtRjg2I1ExJnVtaW51czA7NDUyNjcwOUYoLUY4NiNRMSZ1bWludXMwOzIzMzI1MDJGKEknTWF0cml4R0YlNyMtRmhvNiMvSSQlaWRHRihGMQ== P := Matrix(4,4, [ 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, -M[4,3], M[3,3]] ): M := P.M; 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 P := Matrix(4,4, [ M[4,4], 0, 0, -M[1,4], 0, M[4,4], 0, -M[2,4], 0, 0, M[4,4], -M[3,4], 0, 0, 0, 1] ): M := P.M: P := Matrix(4,4, [ M[3,3], 0, -M[1,3], 0, 0, M[3,3], -M[2,3], 0, 0, 0, 1, 0, 0, 0, 0, 1] ): M := P.M: P := Matrix(4,4, [ M[2,2],-M[1,2], 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1] ): M := P.M: P := ZeroMatrix(4): P[1,1] := 1/(igcd(M[1,1], M[1,5])): P[2,2] := 1/(igcd(M[2,2], M[2,5])): P[3,3] := 1/(igcd(M[3,3], M[3,5])): P[4,4] := 1/(igcd(M[4,4], M[4,5])): M := P.M; LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSJNR0YoLUknUlRBQkxFR0YoNiUiNXEhPkgnM2ZZblc9LUknTUFUUklYR0YoNiM3JjcnLUkjbW5HNiRGJi9JK21vZHVsZW5hbWVHRihGJDYjUSg0MTc1MzUxRigtRjg2I1EiMEYoRj5GPi1GODYjUSYxODY2NUYoNydGPkY3Rj5GPi1GODYjUTEmdW1pbnVzMDszMDg3OTE1Rig3J0Y+Rj4tRjg2I1ExJnVtaW51czA7NDE3NTM1MUYoRj4tRjg2I1EmMTkwNTZGKDcnRj5GPkY+LUY4NiNRMiZ1bWludXMwOzEyNTI2MDUzRigtRjg2I1ExJnVtaW51czA7NjYyOTA3OEYoSSdNYXRyaXhHRiU3Iy1GVjYjL0kkJWlkR0YoRjE= ReducedRowEchelonForm(A); LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyMtSSdSVEFCTEVHRig2JSI1YVsiSCczZlluVz0tSSdNQVRSSVhHRig2IzcmNyctSSNtbkc2JEYmL0krbW9kdWxlbmFtZUdGKEYkNiNRIjFGKC1GNjYjUSIwRihGPEY8LUkmbWZyYWNHRjc2JC1GNjYjUSYxODY2NUYoLUY2NiNRKDQxNzUzNTFGKDcnRjxGNUY8RjwtSSVtcm93R0Y3NiQtSSNtb0dGNzYjUSomdW1pbnVzMDtGKC1GQDYkLUY2NiNRKDMwODc5MTVGKEZFNydGPEY8RjVGPC1GSjYkRkwtRkA2JC1GNjYjUSYxOTA1NkYoRkU3J0Y8RjxGPEY1LUZANiQtRjY2I1EoNjYyOTA3OEYoLUY2NiNRKTEyNTI2MDUzRihJJ01hdHJpeEdGJTcjLUZgbzYjL0kkJWlkR0YoRi8=
<Text-field style="Heading 1" layout="Heading 1"><Font encoding="UTF-8">Conclus\303\243o</Font></Text-field>Nota : Na se\303\247\303\243o Treinamento (modific\303\241vel), instalei os valores para o primeiro uso.
<Text-field style="Heading 1" layout="Heading 1"><Font encoding="UTF-8"> Treinamento (modific\303\241vel)</Font></Text-field> restart: with(Student[LinearAlgebra]): A := Matrix(3,4, [ 3, 2, 3, 4, 5, 6, 7, 8, -9,10,11,12]); M := A: LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSJBR0YoLUknUlRBQkxFR0YoNiUiNVk/P0UzZlluVz0tSSdNQVRSSVhHRig2IzclNyYtSSNtbkc2JEYmL0krbW9kdWxlbmFtZUdGKEYkNiNRIjNGKC1GODYjUSIyRihGNy1GODYjUSI0Rig3Ji1GODYjUSI1RigtRjg2I1EiNkYoLUY4NiNRIjdGKC1GODYjUSI4Rig3Ji1GODYjUSsmdW1pbnVzMDs5RigtRjg2I1EjMTBGKC1GODYjUSMxMUYoLUY4NiNRIzEyRihJJ01hdHJpeEdGJTcjLUZobjYjL0kkJWlkR0YoRjE= M; LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyMtSSdSVEFCTEVHRig2JSI1WT8/RTNmWW5XPS1JJ01BVFJJWEdGKDYjNyU3Ji1JI21uRzYkRiYvSSttb2R1bGVuYW1lR0YoRiQ2I1EiM0YoLUY2NiNRIjJGKEY1LUY2NiNRIjRGKDcmLUY2NiNRIjVGKC1GNjYjUSI2RigtRjY2I1EiN0YoLUY2NiNRIjhGKDcmLUY2NiNRKyZ1bWludXMwOzlGKC1GNjYjUSMxMEYoLUY2NiNRIzExRigtRjY2I1EjMTJGKEknTWF0cml4R0YlNyMtRmZuNiMvSSQlaWRHRihGLw== P := Matrix(3,3, [ 1, 0, 0, -5, 3, 0, 9, 0, 3 ]): M := P.M: igcd(-63, -10, 59, -3); IiIi ReducedRowEchelonForm(A); LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyMtSSdSVEFCTEVHRig2JSI1WU8pSCczZlluVz0tSSdNQVRSSVhHRig2IzclNyYtSSNtbkc2JEYmL0krbW9kdWxlbmFtZUdGKEYkNiNRIjFGKC1GNjYjUSIwRihGPEY8NyZGPEY1RjwtRjY2I1ErJnVtaW51czA7MUYoNyZGPEY8RjUtRjY2I1EiMkYoSSdNYXRyaXhHRiU3Iy1GRzYjL0kkJWlkR0YoRi8=
<Text-field style="Heading 1" layout="Heading 1"><Font encoding="UTF-8"> Treinamento (aleat\303\263rio) </Font></Text-field> restart: with(Student[LinearAlgebra]): randomize(): A := RandomMatrix(3, 4); LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSJBR0YoLUknUlRBQkxFR0YoNiUiNVk/P0UzZlluVz0tSSdNQVRSSVhHRig2IzclNyYtSSNtbkc2JEYmL0krbW9kdWxlbmFtZUdGKEYkNiNRLCZ1bWludXMwOzQwRigtRjg2I1EjNjNGKC1GODYjUSMzN0YoLUY4NiNRIzI2Rig3Ji1GODYjUSwmdW1pbnVzMDs4OEYoLUY4NiNRLCZ1bWludXMwOzU4RigtRjg2I1EjODBGKC1GODYjUSM1NkYoNyYtRjg2I1EsJnVtaW51czA7NzNGKC1GODYjUSwmdW1pbnVzMDs0N0YoLUY4NiNRIzc5RigtRjg2I1EjNzdGKEknTWF0cml4R0YlNyMtRltvNiMvSSQlaWRHRihGMQ== M := A: M; LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyMtSSdSVEFCTEVHRig2JSI1WT8/RTNmWW5XPS1JJ01BVFJJWEdGKDYjNyU3Ji1JI21uRzYkRiYvSSttb2R1bGVuYW1lR0YoRiQ2I1EsJnVtaW51czA7NDBGKC1GNjYjUSM2M0YoLUY2NiNRIzM3RigtRjY2I1EjMjZGKDcmLUY2NiNRLCZ1bWludXMwOzg4RigtRjY2I1EsJnVtaW51czA7NThGKC1GNjYjUSM4MEYoLUY2NiNRIzU2Rig3Ji1GNjYjUSwmdW1pbnVzMDs3M0YoLUY2NiNRLCZ1bWludXMwOzQ3RigtRjY2I1EjNzlGKC1GNjYjUSM3N0YoSSdNYXRyaXhHRiU3Iy1GaW42Iy9JJCVpZEdGKEYv P := Matrix(3,3, [ 1, 0, 0, 0, 1, 0, 0, 0, 1 ]): M := P.M: igcd(-63, -10, 59, -3); IiIi ReducedRowEchelonForm(A); LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyMtSSdSVEFCTEVHRig2JSI1LWojSCczZlluVz0tSSdNQVRSSVhHRig2IzclNyYtSSNtbkc2JEYmL0krbW9kdWxlbmFtZUdGKEYkNiNRIjFGKC1GNjYjUSIwRihGPC1JJm1mcmFjR0Y3NiQtRjY2I1EmNzc5MjdGKC1GNjYjUSY0OTY1NUYoNyZGPEY1RjwtSSVtcm93R0Y3NiQtSSNtb0dGNzYjUSomdW1pbnVzMDtGKC1GQDYkLUY2NiNRJDU1MkYoRkU3JkY8RjxGNS1GQDYkLUY2NiNRJzEyMDA3OEYoRkVJJ01hdHJpeEdGJTcjLUZlbjYjL0kkJWlkR0YoRi8=