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Math Help - Unique Solution

  1. #1
    VkL
    VkL is offline
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    Unique Solution

    Consider the following system:
    x + y + az = 1
    x + ay + z = 4
    ax + y + z = b
    For which values of a does the system have a unique solution, and for which pairs
    of values (a; b) does the system have more than one solution? The value of b does
    not have any e ffect on whether the system has a unique solution. Why?

    How do I go about doing this? It's already in reduced form. Idk what to do =/
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  2. #2
    Math Engineering Student
    Krizalid's Avatar
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    Quote Originally Posted by VkL View Post
    Consider the following system:
    x + y + az = 1
    x + ay + z = 4
    ax + y + z = b
    For which values of a does the system have a unique solution
    put that system into a matrix (augmented form), and let the rank of the augmented matrix be equal to the non augmented matrix and equal to the number of variables.

    Quote Originally Posted by VkL View Post
    and for which pairs
    of values (a; b) does the system have more than one solution? The value of b does
    not have any e ffect on whether the system has a unique solution. Why?
    this a question that you'll probably figure out when you get those ranks, so in this case we require that the rank of the augmented matrix be equal to the non augmented matrix and les than the number of variables.
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  3. #3
    VkL
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    what do you mean

    "let the rank of the augmented matrix be equal to the non augmented matrix"?
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