My Math Forum vector linear independent of some space cocient

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 April 2nd, 2011, 05:45 PM #1 Newbie   Joined: Feb 2011 From: Chile Posts: 14 Thanks: 0 vector linear independent of some space cocient $u=(1,2,3,4)$ and $v=(1,1,1,1)$ generates to every solution of certain system of homogeneus linear equations in 4 uknows. * Type a homogeneous system of linear equations with 4 unknowns that has this set of solutions. My development is: Let $(x_1,x_2)$ all solution of the system. As $u$ and $v$ is generates, we have: $\alpha_1(1,2,3,4)+\alpha_2(1,1,1,1)=(x_1,x_2)$ From here, should I stop $x_1$ and $x_2$ in terms of scalar? Thanks in advance. $u=(1,2,3,4)$ and $v=(1,1,1,1)$ genera a toda solucion de cierto sistema de ecuaciones lineales homogéneo en 4 incógnitas *Escriba un sistema de ecuaciones lineal homogéneo con 4 incógnitas que contenga a ese conjunto de soluciones. Mi desarollo es: Sea $(x_1,x_2)$ toda solución del sistema Como $u$ y $v$ lo genera, tenemos que: $\alpha_1(1,2,3,4)+\alpha_2(1,1,1,1)=$$(x_1,x_2)$ "De aqui, ¿Débo dejar $x_1$ y $x_2$ en función de los escalares? Gracias de antemano

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### cocient

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