DETERMINANTES DE MATRIZES
Estudando Determinantes
Associado a toda matriz quadrada M (n x n) est\303\241 um n\303\272mero real chamado determinante de M , indicado por det(M) ou| M | . Para uma matriz M (2 x 2) onde M = 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, o determinante de M \303\251 dado por det M = | M | = ad - bc.Para a matriz M 2 x 2 definida abaixo, o det(M) ser\303\241 encontrado.LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYqLUkjbWlHRiQ2JVEocmVzdGFydEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIjtGJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRjEvJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdRLDAuMjc3Nzc3OGVtRictRjY2LVEifkYnRjlGOy9GP0Y9RkBGQkZERkZGSEZKL0ZORkwtRiw2JVEld2l0aEYnRi9GMi1JKG1mZW5jZWRHRiQ2JC1GIzYlLUYsNiVRJ2xpbmFsZ0YnRi9GMi8lK2V4ZWN1dGFibGVHRj1GOUY5LUY2Ni1RIjpGJ0Y5RjtGU0ZARkJGREZGRkgvRktGT0ZNRmpuRjk=LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYvLUkjbW9HRiQ2LVEifkYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGNC8lKXN0cmV0Y2h5R0Y0LyUqc3ltbWV0cmljR0Y0LyUobGFyZ2VvcEdGNC8lLm1vdmFibGVsaW1pdHNHRjQvJSdhY2NlbnRHRjQvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZDLUkjbWlHRiQ2JVEiTUYnLyUnaXRhbGljR1EldHJ1ZUYnL0YwUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2Ji1GIzYlLUkjbW5HRiQ2JFEiMUYnRi8vJStleGVjdXRhYmxlR0Y0Ri9GLy8lJW9wZW5HUSJbRicvJSZjbG9zZUdRIl1GJy1GLDYtUSomY29sb25lcTtGJ0YvRjJGNUY3RjlGO0Y9Rj8vRkJRLDAuMjc3Nzc3OGVtRicvRkVGXm8tRkc2JVEnbWF0cml4RidGSkZNLUZQNiQtRiM2KS1GVTYkUSIyRidGLy1GLDYtUSIsRidGL0YyL0Y2RkxGN0Y5RjtGPUY/RkEvRkVRLDAuMzMzMzMzM2VtRidGZ29Gam8tRlA2Ji1GIzYtLUYsNi1RKiZ1bWludXMwO0YnRi9GMkY1RjdGOUY7Rj1GPy9GQlEsMC4yMjIyMjIyZW1GJy9GRUZocC1GVTYkUSIzRidGL0Zqb0Znb0Zqby1GVTYkUSI1RidGL0Zqb0ZkcC1GVTYkUSI4RidGL0ZYRi9GL0ZaRmduRlhGL0YvLUYsNi1RIjtGJ0YvRjJGXXBGN0Y5RjtGPUY/RkFGX28tSSdtc3BhY2VHRiQ2Ji8lJ2hlaWdodEdRJjAuMGV4RicvJSZ3aWR0aEdGQy8lJmRlcHRoR0Zbci8lKmxpbmVicmVha0dRJWF1dG9GJy1GZ3E2JkZpcUZcckZeci9GYXJRKG5ld2xpbmVGJ0ZmcS1GRzYjUSFGJ0ZYRi8=LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYsLUkjbW9HRiQ2LVEifkYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGNC8lKXN0cmV0Y2h5R0Y0LyUqc3ltbWV0cmljR0Y0LyUobGFyZ2VvcEdGNC8lLm1vdmFibGVsaW1pdHNHRjQvJSdhY2NlbnRHRjQvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZDLUkjbWlHRiQ2JVEkZGV0RicvJSdpdGFsaWNHUSV0cnVlRicvRjBRJ2l0YWxpY0YnLUkobWZlbmNlZEdGJDYkLUYjNiYtRkc2JVEiTUYnRkpGTS1GUDYmLUYjNiUtSSNtbkdGJDYkUSIxRidGLy8lK2V4ZWN1dGFibGVHRjRGL0YvLyUlb3BlbkdRIltGJy8lJmNsb3NlR1EiXUYnRmluRi9GLy1GLDYtUSI7RidGL0YyL0Y2RkxGN0Y5RjtGPUY/RkEvRkVRLDAuMjc3Nzc3OGVtRictSSdtc3BhY2VHRiQ2Ji8lJ2hlaWdodEdRJjAuMGV4RicvJSZ3aWR0aEdGQy8lJmRlcHRoR0ZccC8lKmxpbmVicmVha0dRJWF1dG9GJy1GaG82JkZqb0ZdcEZfcC9GYnBRKG5ld2xpbmVGJ0Znby1GRzYjUSFGJ0ZpbkYvO Maple V \303\251 em particular ben\303\251fico quando se deseja calcular determinantes de ordem superior. Considere a matriz (M) 5 x 5 no qual o valor de seu determinante \303\251 solicitado.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Qual o determinante de LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEiTUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21uR0YkNiRRIjJGJy9GNlEnbm9ybWFsRicvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJy1GLzYjUSFGJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnRjw=?
R: det( LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYpLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEiTUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21uR0YkNiRRIjJGJy9GNlEnbm9ybWFsRicvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJy1GLzYjUSFGJy8lK2ZvcmVncm91bmRHUSpbMCwwLDI1NV1GJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnLyUpcmVhZG9ubHlHRjQvJTBmb250X3N0eWxlX25hbWVHUSoyRH5PdXRwdXRGJ0Y8) = 174Considere a situa\303\247\303\243o em que uma equa\303\247\303\243o envolvendo um determinante possa ser resolvida.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Qual o valor de x ?
R: -5Aplica\303\247\303\265es de Determinantes
Os Determinantes podem ser usados para encontrar a equa\303\247\303\243o de uma linha passando por dois pontos dados. Dados dois pontos P(a,b) e Q(c,d), a equa\303\247\303\243o para a linha PQ pode ser escrita como :A equa\303\247\303\243o da linha que passa pelos pontos P(1,4) e Q(2,0) \303\251 encontrada como se segue.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Determine a equa\303\247\303\243o da linha que passa pelos pontos R(-1,1) e S(5,3) .
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R: LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYpLUkjbWlHRiQ2JVEieUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIj1GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1GNjYtUSJ+RidGOUY7Rj5GQEZCRkRGRkZIL0ZLUSYwLjBlbUYnL0ZORlMtRiM2Ki1JJm1mcmFjR0YkNigtSSNtbkdGJDYkUSI0RidGOS1GZW42JFEiM0YnRjkvJS5saW5ldGhpY2tuZXNzR1EiMUYnLyUrZGVub21hbGlnbkdRJ2NlbnRlckYnLyUpbnVtYWxpZ25HRmBvLyUpYmV2ZWxsZWRHRj0tRjY2LVEnJnBsdXM7RidGOUY7Rj5GQEZCRkRGRkZIL0ZLUSwwLjIyMjIyMjJlbUYnL0ZORmlvLUZYNigtRiw2JVEieEYnRi9GMkZobkZbb0Zeb0Zhb0Zjby8lK2ZvcmVncm91bmRHUSpbMCwwLDI1NV1GJy8lK2V4ZWN1dGFibGVHRj0vJSlyZWFkb25seUdGMS8lMGZvbnRfc3R5bGVfbmFtZUdRKjJEfk91dHB1dEYnRjktRiw2I1EhRidGY3BGOQ==LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbW9HRiQ2LVEifkYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGNC8lKXN0cmV0Y2h5R0Y0LyUqc3ltbWV0cmljR0Y0LyUobGFyZ2VvcEdGNC8lLm1vdmFibGVsaW1pdHNHRjQvJSdhY2NlbnRHRjQvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZDLyUrZXhlY3V0YWJsZUdGNEYvLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbW9HRiQ2LVEifkYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGNC8lKXN0cmV0Y2h5R0Y0LyUqc3ltbWV0cmljR0Y0LyUobGFyZ2VvcEdGNC8lLm1vdmFibGVsaW1pdHNHRjQvJSdhY2NlbnRHRjQvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZDLyUrZXhlY3V0YWJsZUdGNEYvOs Determinantes tamb\303\251m podem ser usados para encontrar a \303\241rea de um tri\303\242ngulo quando as coordenadas dos v\303\251rtices s\303\243o conhecidas. A Lagrangeana matem\303\241tica \303\251 respons\303\241vel pelo desenvolvimento da f\303\263rmula para o c\303\241lculo da \303\241rea de um tri\303\242ngulo atrav\303\251s do determinante. Em geral, a \303\241rea do triangulo MNO com v\303\251rtices M, N, e O \303\251 :Os pontos devem ser pegos na ordem inversa ao ponteiro do rel\303\263gio para produzir um valor positivo para a \303\241rea. Alternadamente, o valor absoluto da metade do determinante pode ser obtido.
O tri\303\242ngulo de v\303\251rtices M(0,1), N(1,4), e O(2,0) est\303\241 apresentado no gr\303\241fico abaixo.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A \303\241rea do tri\303\242ngulo formado pela conex\303\243o dos v\303\251rtices \303\251 encontrada como se segue:
LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEocmVzdGFydEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIjtGJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRjEvJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJStleGVjdXRhYmxlR0Y9Rjk=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Determine a \303\241rea do tr\303\242angulo com v\303\251rtices P(2, -2), Q(0,0), e R(-3, -4).
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