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 2 years ago
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
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?

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

satellite73
 2 years ago
Best ResponseYou've already chosen the best response.1i am not sure, but since you have the matrix there, maybe you could take the determinate, set it equal to zero and solve for \(a\)

frx
 2 years ago
Best ResponseYou've already chosen the best response.0If 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?

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

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

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