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Math Help - Homogeneous system solution

  1. #1
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    Homogeneous system solution

    I am in a matrices and power function class,

    we are asked to determine if this homogeneous system has a unique solution without explicitly solving it.

    -x + 2y - z = 0

    2x + y + z = 0

    x - y + 2z = 0

    So, I setup the matrix and checked that the determinant does not equal 0. It does not, it is - 4. Then the question wants me to give the values for x,y and z without solving for them based on what I already know.

    The values, it says, are x = y = z = 0

    Can someone please tell me how I am to know this????
    Thanks Frostking
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  2. #2
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    Quote Originally Posted by Frostking View Post
    I am in a matrices and power function class,

    we are asked to determine if this homogeneous system has a unique solution without explicitly solving it.

    -x + 2y - z = 0

    2x + y + z = 0

    x - y + 2z = 0

    So, I setup the matrix and checked that the determinant does not equal 0. It does not, it is - 4. Then the question wants me to give the values for x,y and z without solving for them based on what I already know.

    The values, it says, are x = y = z = 0

    Can someone please tell me how I am to know this????
    Thanks Frostking
    Since the coeffient matrix is invertable you know the system has Exactly 1 unique solution. Homogenous systems always have the trivial solution. x=y=z=0.

    Combining these two facts gives you what you want.

    Putting these two
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