MATRIZES E SISTEMAS DE EQUA\303\207\303\225ES LINEARES
Pesquisando Matriz Identidade e Matriz InversaUma matriz quadrada de ordem n que possui todos os elementos da diagonal principal iguais a 1 e os outros elementos iguais a zero \303\251 chamada matriz identidade. A matriz identidade de ordem n \303\251 indicada por LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEiSkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnL0YzUSdub3JtYWxGJw==e tem propriedades semelhantes ao n\303\272mero real 1. Por exemplo, o produto de uma matriz M e LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEiSkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnL0YzUSdub3JtYWxGJw== \303\251 M, assim como o produto de um n\303\272mero x e 1 \303\251 x .No exemplo abaixo colocamos a matriz identidade como J, pois I \303\251 uma vari\303\241vel protegida do Maple V .LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEocmVzdGFydEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIjtGJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRjEvJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJStleGVjdXRhYmxlR0Y9Rjk=LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JVEld2l0aEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzYlLUYsNiVRJ2xpbmFsZ0YnRi9GMi8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnL0YzUSdub3JtYWxGJ0ZALUkjbW9HRiQ2LVEiOkYnRkAvJSZmZW5jZUdGPy8lKnNlcGFyYXRvckdGPy8lKXN0cmV0Y2h5R0Y/LyUqc3ltbWV0cmljR0Y/LyUobGFyZ2VvcEdGPy8lLm1vdmFibGVsaW1pdHNHRj8vJSdhY2NlbnRHRj8vJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZWRj1GQA==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Note que os produtos resultantes s\303\243o ambos id\303\252nticos a matriz original M.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O que pode ser conclu\303\255do sobre as matrizes B e C?
R: As matrizes B e C s\303\243o inversas.plicando Matrizes Inversas para Solucionar Sistemas Lineares
Considere a situa\303\247\303\243o em que a equa\303\247\303\243o do polin\303\264mio c\303\272bico que passa pelos pontos ( - 2 , - 28) , ( - 1 , - 10) , (1, - 4) e (3 , 2 ) \303\251 necess\303\241ria. Lembre-se que estes 4 pontos devem satisfazer o polin\303\264mio c\303\272bico.O processo para encontrar a equa\303\247\303\243o desejada come\303\247a expressando P como y e substituindo cada valor de x e y na equa\303\247\303\243o c\303\272bica geral .LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEocmVzdGFydEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIjtGJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRjEvJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJStleGVjdXRhYmxlR0Y9Rjk=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Estas quatro equa\303\247\303\265es resultantes formam um sistema que pode ser facilmente solucionado usando matrizes. Contudo, a matriz coeficiente A , a matriz constante B , e a matriz vari\303\241vel X devem ser definidas 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LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbW9HRiQ2LVEifkYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGNC8lKXN0cmV0Y2h5R0Y0LyUqc3ltbWV0cmljR0Y0LyUobGFyZ2VvcEdGNC8lLm1vdmFibGVsaW1pdHNHRjQvJSdhY2NlbnRHRjQvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZDLyUrZXhlY3V0YWJsZUdGNEYvPara solucionar o sistema usando matrizes, o produto deve ser encontrado.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Alexis e Alex s\303\243o gemeos que acabaram de passar na prova de tr\303\242nsito e agora querem ganhar um carro de seu pai. Este n\303\243o tem dinheiro dispon\303\255vel para comprar o carro, mas prometeu pegar dinheiro emprestado com cart\303\265es de cr\303\251dito que possuam baixa taxa de juros. O pai decidiu pegar emprestado $9600 de tr\303\252s cart\303\265es de cr\303\251ditos diferentes com taxa de juros anual de 5.9% , 7.5% e 6.7% , respectivamente. Ele pegou emprestado tr\303\252s vezes a mais no cart\303\243o de 5.9% do que no cart\303\243o de 7.5% , e o juros anual total dos tr\303\252s cart\303\265es \303\251 $644.60. Quanto o pai deles pegou emprestado de cada cart\303\243o de cr\303\251dito?
Seja x o valor pego no cart\303\243o de 5.9% , y o valor pego no cart\303\243o de 7.5% , e z o valor pego no cartao de 6.7%. Lembre-se que o juros anual total \303\251 $644.60, o valor total pego emprestado \303\251 $9600, e que foi pego emprestado tr\303\252s vezes a mais no cart\303\243o de 5.9 % do que no cart\303\243o de 7.5 % .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 a matriz coeficiente representada por F, a matriz constante representada por G, e a matriz vari\303\241vel representada por X.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-se que para solucionar um sistema usando matrizes \303\251 necess\303\241rio encontrar o produtoLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYsLUkjbWlHRiQ2JVEmZXZhbG1GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSShtZmVuY2VkR0YkNiQtRiM2Ky1GLDYlUSJYRidGL0YyLUkjbW9HRiQ2LVEiPUYnL0YzUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGRS8lKXN0cmV0Y2h5R0ZFLyUqc3ltbWV0cmljR0ZFLyUobGFyZ2VvcEdGRS8lLm1vdmFibGVsaW1pdHNHRkUvJSdhY2NlbnRHRkUvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZULUYsNiVRIkZGJ0YvRjItRj42LVEiXkYnRkFGQ0ZGRkhGSkZMRk5GUC9GU1EsMC4xMTExMTExZW1GJy9GVkZobi1GNjYkLUYjNiYtRj42LVEqJnVtaW51czA7RidGQUZDRkZGSEZKRkxGTkZQL0ZTUSwwLjIyMjIyMjJlbUYnL0ZWRmJvLUkjbW5HRiQ2JFEiMUYnRkEvJStleGVjdXRhYmxlR0ZFRkFGQS1GPjYtUSMmKkYnRkFGQ0ZGRkhGSkZMRk5GUC9GU1EmMC4wZW1GJy9GVkZecC1GLDYlUSJHRidGL0YyRmhvRkFGQS1GPjYtUSI7RidGQUZDL0ZHRjFGSEZKRkxGTkZQRl1wRlUtSSdtc3BhY2VHRiQ2Ji8lJ2hlaWdodEdRJjAuMGV4RicvJSZ3aWR0aEdGXnAvJSZkZXB0aEdGXHEvJSpsaW5lYnJlYWtHUShuZXdsaW5lRictRmhwNiZGanBGXXFGX3EvRmJxUSVhdXRvRidGZ3BGZHEtRiw2I1EhRidGaG9GQQ==Quanto o pai deles pediu emprestado a cada cart\303\243o de cr\303\251dito?
R: $ 87.50 no cart\303\243o de 5.9%
$ 262.50 no cart\303\243o de 7.5%
$ 9,250.00 no cart\303\243o de 6.7%Aplica\303\247\303\265es de Matrizes
Criptografia \303\251 a ci\303\252ncia que visa escrever ou decifrar c\303\263digos. Empresas e uma grande quantidade de corpora\303\247\303\265es de dados computadorizados acham isso necess\303\241rio para ocultar o significado de uma mensagem protegendo uma informa\303\247\303\243o importante contra o roubo por parte dos competidores. Opera\303\247\303\265es matriciais s\303\243o usadas para codificar e decodificar mensagens.
Suponha que voce queira codificar a mensagem MATRICES ARE FRIENDLY. Quando a mensagem \303\251 quebrada em unidades de tamanhos iguais, do tipo duas letras, obtemos o seguinte:
MA TR IC ES AR EF RI EN DL YZ
(The Z at the end is there only to hold a place.)
A cada letra do alfabeto \303\251 fixado um equivalente num\303\251rico.
A B C D E F G H I J K L M N O P Q R S T U V W X Y Z
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 263Escolha qualquer matriz J 2 x 2 que possua inversa.LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEocmVzdGFydEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIjtGJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRjEvJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJStleGVjdXRhYmxlR0Y9Rjk=LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JVEld2l0aEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzYlLUYsNiVRJ2xpbmFsZ0YnRi9GMi8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnL0YzUSdub3JtYWxGJ0ZALUkjbW9HRiQ2LVEiOkYnRkAvJSZmZW5jZUdGPy8lKnNlcGFyYXRvckdGPy8lKXN0cmV0Y2h5R0Y/LyUqc3ltbWV0cmljR0Y/LyUobGFyZ2VvcEdGPy8lLm1vdmFibGVsaW1pdHNHRj8vJSdhY2NlbnRHRj8vJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZWRj1GQA==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Agora multiplique cada matriz coluna a esquerda por J. J \303\251 chamada matriz codificada.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A nova mensagem codificada \303\251 31 16 130 74 33 18 105 62 92 55 40 23 81 45 80 47 68 40 180 103.
Agora suponha que voc\303\252 queira decodificar a mensagem codificada. Inverta o processo acima e reescreva a nova mensagem codificada como matrizes coluna 2 x 1 e ent\303\243o multiplique a esquerda cada matriz coluna por LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUklbXN1cEdGJDYlLUkjbWlHRiQ2JVEiSkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYmLUkjbW9HRiQ2LVEqJnVtaW51czA7RicvRjZRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0ZCLyUpc3RyZXRjaHlHRkIvJSpzeW1tZXRyaWNHRkIvJShsYXJnZW9wR0ZCLyUubW92YWJsZWxpbWl0c0dGQi8lJ2FjY2VudEdGQi8lJ2xzcGFjZUdRLDAuMjIyMjIyMmVtRicvJSdyc3BhY2VHRlEtSSNtbkdGJDYkUSIxRidGPkYyRjUvJTFzdXBlcnNjcmlwdHNoaWZ0R1EiMEYnLyUrZXhlY3V0YWJsZUdGQkY+. .(Sem o conhecimento da matriz J, decodificar a mensagem seria muito dif\303\255cil.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etc..
Usando o alfabeto num\303\251rico acima, determine as primeiras seis letras da mensagem decodificada.
R: Matriz .Obs: Qualque matriz 2 x 2 que possua inversa pode ser usada.LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEocmVzdGFydEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIjtGJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRjEvJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJStleGVjdXRhYmxlR0Y9Rjk=LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JVEld2l0aEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzYlLUYsNiVRJ2xpbmFsZ0YnRi9GMi8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnL0YzUSdub3JtYWxGJ0ZALUkjbW9HRiQ2LVEiOkYnRkAvJSZmZW5jZUdGPy8lKnNlcGFyYXRvckdGPy8lKXN0cmV0Y2h5R0Y/LyUqc3ltbWV0cmljR0Y/LyUobGFyZ2VvcEdGPy8lLm1vdmFibGVsaW1pdHNHRj8vJSdhY2NlbnRHRj8vJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZWRj1GQA==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: 30 24 37 22 39 20 41 23 32 25 15 10 52 38.
Dada a matriz decodificada U definida abaixo, decifre a seguinte mensagem.
1 63 100 3 19 17 0 51 81 17 117 115 9 96 115 - 17 52 158LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEocmVzdGFydEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIjtGJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRjEvJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJStleGVjdXRhYmxlR0Y9Rjk=LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JVEld2l0aEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzYlLUYsNiVRJ2xpbmFsZ0YnRi9GMi8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnL0YzUSdub3JtYWxGJ0ZALUkjbW9HRiQ2LVEiOkYnRkAvJSZmZW5jZUdGPy8lKnNlcGFyYXRvckdGPy8lKXN0cmV0Y2h5R0Y/LyUqc3ltbWV0cmljR0Y/LyUobGFyZ2VvcEdGPy8lLm1vdmFibGVsaW1pdHNHRj8vJSdhY2NlbnRHRj8vJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZWRj1GQA==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O que diz a mensagem decodificada?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R: BASEBALL \303\211 CHATO.