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frx

  • 2 years ago

For which values of the constant a does the equationsystem have infinty many solutions and then doesn't any solutions exist. \[ax _{1} +(a-1)x _{2}+(a-2)x _{3}=0\] \[(a-3)x _{2}+(a-4)x _{3}=1\] \[(a-5)x _{3}=0\] 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?

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  1. frx
    • 2 years ago
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    \[\left[\begin{matrix}a & a-1&a-2 \\ 0 & a-3&a-4 \\ 0&0&a-5\end{matrix}\right]\]

  2. frx
    • 2 years ago
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    @satellite73

  3. satellite73
    • 2 years ago
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    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 \(a\)

  4. frx
    • 2 years ago
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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?

  5. satellite73
    • 2 years ago
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    the determinant is \(a(a-3)(a-5)\) so maybe no solution if \(a=0,a=3,a=5\)

  6. frx
    • 2 years ago
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    The key says a=0 and a=3 so that seems to be right

  7. satellite73
    • 2 years ago
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    whew

  8. frx
    • 2 years ago
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    Hehe so now I know the way to solve these are by using the determinant, thank you satellite73, helpful as always :)

  9. satellite73
    • 2 years ago
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    yw

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