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For which values of the constant a does the equationsystem have infinty many solutions and then doesn't any solutions exist. \[ax _{1} +(a-1)x _{2}+(a-2)x _{3}=0\] \[(a-3)x _{2}+(a-4)x _{3}=1\] \[(a-5)x _{3}=0\] Well I know that the system has infinity many solutions when a=5 but what should I look for then searching for the values there no solutions exist?

Mathematics
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\[\left[\begin{matrix}a & a-1&a-2 \\ 0 & a-3&a-4 \\ 0&0&a-5\end{matrix}\right]\]
i am not sure, but since you have the matrix there, maybe you could take the determinate, set it equal to zero and solve for \(a\)

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If i rember correct then infinity is when the matrix get a full row of zeros and no solution then matrix gets a row of zeros but the answer isn't zero, do you think that can be right?
the determinant is \(a(a-3)(a-5)\) so maybe no solution if \(a=0,a=3,a=5\)
The key says a=0 and a=3 so that seems to be right
whew
Hehe so now I know the way to solve these are by using the determinant, thank you satellite73, helpful as always :)
yw

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