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Math Help - Homogeneous system

  1. #1
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    Homogeneous system

    How do I show that a homogeneous system of linear equations, where all of the coefficients of one of the unknowns is zero, has a non-zero solution?
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  2. #2
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    Quote Originally Posted by nzmathman View Post
    How do I show that a homogeneous system of linear equations, where all of the coefficients of one of the unknowns is zero, has a non-zero solution?
    Say among the variables x_1,x_2,...,x_n the x_k variable have all its cofficients to be zero. Then you can let x_k be whatever you wish it to be i.e. let x_1=x_2= ... = x_{k-1} = 0, x_k = t, x_{k+1} = ... = x_n = 0 where t\in \mathbb{R}.
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    Ah, that makes sense. Thanks!
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