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Math Help - solution space

  1. #1
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    solution space

    Is only a homogeneous system may have a solution space?
    Thanks in advance...
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  2. #2
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    Re: solution space

    Yes, because the set of solutions of a non-homogeneous system is not closed under addition and, therefore, is not a vector space.
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  3. #3
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    Re: solution space

    Specifically, if u and v satisfy Ax= 0, then A(au+ bv)= aA(u)+ bA(v)= 0 but they satisfy Ax= p, where p is not 0, then A(au+ bv)= ap+ bp= (a+ b)p which is not, in general, equal to p.
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