Questões (sistemas Lineares):
Autor: T206-3MF | Publicado: 2012-02-15T12:18:00-08:00

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01. Resolver o sistema abaixo pela Regra de Cramer.


02.    Resolver o sistema abaixo pela Regra de Cramer.


03.    (UESP) Se o terno (x0, y0, z0) é a solução do sistema abaixo, então 3x0 + 5y0 + 4z0 é igual a:

 &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; a) -8
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; b) -7
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; c) -6
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; d) -5
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; e) -4


04.    Calcular a característica da matriz abaixo:


05.    O sistema abaixo:&nbsp; 

 &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; a) só apresenta a solução trivial;
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; b) é possível e determinado não tendo solução trivial;
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; c) é possível e indeterminado;
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; d) é impossível;
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; e) admite a solução (1; 2; 1) 


06.    O sistema abaixo:&nbsp; 

 &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; a) é impossível;
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; b) é possível e determinado;
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; c) é possível e indeterminado;
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; d) admite apenas a solução (1; 2; 3);
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; e) admite a solução (2; 0; 0) 


07.    (UEL) O sistema abaixo, de incógnitas x e y, é:

 &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; a) impossível, para todo k real diferente de -21;
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; b) possível e indeterminado, para todo k real diferente de -63;
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; c) possível e determinado, para todo k real diferente de -21;
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; d) possível e indeterminado, para todo k real diferente de -3;
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; e) possível e determinado, para todo k real diferente de -1 e -63. 


08.    Considere o seguinte sistema de equações de incógnitas x e y:&nbsp; Esse sistema tem uma única solução para certo número real k que é um: 

 &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; a) quadrado perfeito
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; b) número primo
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; c) número racional não inteiro
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; d) número negativo
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; e) múltiplo de 5 


09.    Se tivermos o sistema abaixo, então x + y + z + t é igual a:

 &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; a) -1
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; b) 7
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; c) 5
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; d) 4
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; e) 5/9 


10.    Determinar m para que o sistema abaixo tenha apenas a solução trivial.



Resolução: 
01 - (2; 3)02 - (1; 2; 3)
      03 - B      04 - 3
      05 - D
      06 - C
  
      07 - C
      08 - A
      09 - C      10 - m ¹ 4