URGENTE!!!! AJUDA COM SISTEMA LINEAR
Anexos:
Soluções para a tarefa
Respondido por
1
Boa noite!
Solução!
Para saber se x1,y1 e z1 são soluções basta substituir os valores no sistema.
![2x+3y-z=0\\
x-4y+5z=0\\\\\\\
Substituindo!\\\\\\\
x_{1}=1~~~~y_{1}=-1~~~~z_{1}=-1 \\\\\\\\\\
2(1)+3(-1)-(-1)=0\\
1-4(-1)+5(-1)=0\\\\\\\
2-3+1=0\\
1+4-5=0\\\\\\\
3-3=0\\
-4+4=0\\\\\\\
0=0\\
0=0\\\\\\\
x_{1}=1~~~~y_{1}=-1~~~~z_{1}=-1~~Verdadeiro~~e~~soluc\~ao](https://tex.z-dn.net/?f=2x%2B3y-z%3D0%5C%5C%0Ax-4y%2B5z%3D0%5C%5C%5C%5C%5C%5C%5C%0ASubstituindo%21%5C%5C%5C%5C%5C%5C%5C%0A+x_%7B1%7D%3D1%7E%7E%7E%7Ey_%7B1%7D%3D-1%7E%7E%7E%7Ez_%7B1%7D%3D-1+%5C%5C%5C%5C%5C%5C%5C%5C%5C%5C%0A2%281%29%2B3%28-1%29-%28-1%29%3D0%5C%5C%0A1-4%28-1%29%2B5%28-1%29%3D0%5C%5C%5C%5C%5C%5C%5C%0A+2-3%2B1%3D0%5C%5C%0A1%2B4-5%3D0%5C%5C%5C%5C%5C%5C%5C%0A%0A3-3%3D0%5C%5C%0A-4%2B4%3D0%5C%5C%5C%5C%5C%5C%5C%0A0%3D0%5C%5C%0A0%3D0%5C%5C%5C%5C%5C%5C%5C%0A%0Ax_%7B1%7D%3D1%7E%7E%7E%7Ey_%7B1%7D%3D-1%7E%7E%7E%7Ez_%7B1%7D%3D-1%7E%7EVerdadeiro%7E%7Ee%7E%7Esoluc%5C%7Eao "2x+3y-z=0\\
x-4y+5z=0\\\\\\\
Substituindo!\\\\\\\
x_{1}=1~~~~y_{1}=-1~~~~z_{1}=-1 \\\\\\\\\\
2(1)+3(-1)-(-1)=0\\
1-4(-1)+5(-1)=0\\\\\\\
2-3+1=0\\
1+4-5=0\\\\\\\
3-3=0\\
-4+4=0\\\\\\\
0=0\\
0=0\\\\\\\
x_{1}=1~~~~y_{1}=-1~~~~z_{1}=-1~~Verdadeiro~~e~~soluc\~ao")
O mesmo para os outros valores.
![2x+3y-z=0\\
x-4y+5z=0\\\\\\\
2(-2)+3(2)-2=0\\
-2-4(2)+5(2)=0\\\\\\\
-4+6-2=0\\
-2-8+10=0\\\\\\\
-4-2+6=0\\
-2-8+10=0\\\\\\\
-6+6=0\\
-2-8+10=0\\\\\\\
0=0\\
0=0\\\\\\\
Verdadeiro~~e~~soluc\~ao.](https://tex.z-dn.net/?f=2x%2B3y-z%3D0%5C%5C%0A+x-4y%2B5z%3D0%5C%5C%5C%5C%5C%5C%5C%0A2%28-2%29%2B3%282%29-2%3D0%5C%5C%0A+-2-4%282%29%2B5%282%29%3D0%5C%5C%5C%5C%5C%5C%5C%0A%0A-4%2B6-2%3D0%5C%5C%0A+-2-8%2B10%3D0%5C%5C%5C%5C%5C%5C%5C%0A%0A-4-2%2B6%3D0%5C%5C%0A+-2-8%2B10%3D0%5C%5C%5C%5C%5C%5C%5C%0A%0A-6%2B6%3D0%5C%5C%0A+-2-8%2B10%3D0%5C%5C%5C%5C%5C%5C%5C%0A%0A%0A0%3D0%5C%5C%0A+0%3D0%5C%5C%5C%5C%5C%5C%5C%0AVerdadeiro%7E%7Ee%7E%7Esoluc%5C%7Eao. "2x+3y-z=0\\
x-4y+5z=0\\\\\\\
2(-2)+3(2)-2=0\\
-2-4(2)+5(2)=0\\\\\\\
-4+6-2=0\\
-2-8+10=0\\\\\\\
-4-2+6=0\\
-2-8+10=0\\\\\\\
-6+6=0\\
-2-8+10=0\\\\\\\
0=0\\
0=0\\\\\\\
Verdadeiro~~e~~soluc\~ao.")
Boa noite!
Bons estudos!
Solução!
Para saber se x1,y1 e z1 são soluções basta substituir os valores no sistema.
O mesmo para os outros valores.
Boa noite!
Bons estudos!
Respondido por
1
Este sistema é indeterminado (tem infinitas soluções). Para verificar se uma terna é solução basta substituir as variáveis pelos números (correspondentes) da terna se a igualdade ficar verdadeira é solução.
Ver anexo.
Ver anexo.
Anexos:
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