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I came across a task, which is hard to move for myself (just 1st year of math studies). It is: For what $t\in \mathbb{R}$ set of solutions is a subspace of a $\mathbb{R}^{3}$
$\\ \\3x_{1}+(1-t^{2}){x_{2}}^{3}-x_{3}=0\\ \\x_{1}-5x_{2}+2(t+1)\left |x_{3} \right |=t^{3}-t$ I actually solved it for $t=-1$; then the cube term with in first equation vanishes (altogether with absolute value in second) and then the quest is easy. But what for other $t?$ Do you have any ideas? Thanks in advance!

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Clearly the zero vector needs to be part of the solution. This means the latter equation must satisfy $t^3 - t = 0$. This immediately give you all the candidates as $t=0,\ 1,\ -1$.

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    Alright, thank you very much; now there is no problem with it :-)2012-10-30