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Math Help - Show that if Ax=b has more than 1 solution, it has infinitly many solutions

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    Member Jskid's Avatar
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    Show that if Ax=b has more than 1 solution, it has infinitly many solutions

    Show that if Ax=b has more than 1 solution, it has infinitly many solutions.

    Hint: If u_1 and u_2 are two solutions consider w=ru_1+su_2 where r+s=1

    Here's my start
    let u_1 and u_2 be distinct solutions to Ax=b then Au_1=b and Au_2=b

    Why must r+s=1?
    Last edited by mr fantastic; January 25th 2011 at 07:38 PM. Reason: Copied title into main body, fixed math tag.
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  2. #2
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    Quote Originally Posted by Jskid View Post
    Hint: If u_1 and u_2 are two solutions consider w=ru_1+su_2 where r+s=1

    Here's my start
    let u_1 and u_2 be distinct solutions to Ax=b then [maht]Au_1=b[/tex] and Au_2=b

    Why must r+s=1?
    A(r u_1 + su_2) = b (r + s) ....
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