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frx
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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.
\[ax _{1} +(a1)x _{2}+(a2)x _{3}=0\]
\[(a3)x _{2}+(a4)x _{3}=1\]
\[(a5)x _{3}=0\]
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?
 2 years ago
 2 years ago
frx Group Title
For which values of the constant a does the equationsystem have infinty many solutions and then doesn't any solutions exist. \[ax _{1} +(a1)x _{2}+(a2)x _{3}=0\] \[(a3)x _{2}+(a4)x _{3}=1\] \[(a5)x _{3}=0\] 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?
 2 years ago
 2 years ago

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frx Group TitleBest ResponseYou've already chosen the best response.0
\[\left[\begin{matrix}a & a1&a2 \\ 0 & a3&a4 \\ 0&0&a5\end{matrix}\right]\]
 2 years ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.1
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 \(a\)
 2 years ago

frx Group TitleBest ResponseYou've already chosen the best response.0
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?
 2 years ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.1
the determinant is \(a(a3)(a5)\) so maybe no solution if \(a=0,a=3,a=5\)
 2 years ago

frx Group TitleBest ResponseYou've already chosen the best response.0
The key says a=0 and a=3 so that seems to be right
 2 years ago

frx Group TitleBest ResponseYou've already chosen the best response.0
Hehe so now I know the way to solve these are by using the determinant, thank you satellite73, helpful as always :)
 2 years ago
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