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Math Help - Linear Equations

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    Linear Equations

    If the coefficient matrix of a system of m linear equations in n unknowns has rank m, then the system has a solution?

    Is that true or false?

    I think it is true, consider Ax = b, with rank(A) = m, then rank (A|b) = m, then the system is consistent.

    Is that reasonable?
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  2. #2
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    Quote Originally Posted by tttcomrader View Post
    If the coefficient matrix of a system of m linear equations in n unknowns has rank m, then the system has a solution?

    Is that true or false?

    I think it is true, consider Ax = b, with rank(A) = m, then rank (A|b) = m, then the system is consistent.

    Is that reasonable?
    No.

    It's only true when n = m. For n > m it may or may not be true.

    Consider the really simple example

    x + y = 1

    x + y = 2

    m = 1, n = 2. Is there a solution?


    Consider the really simple example

    x + y = 1

    2x + 2y = 2.

    m = 1, n = 2. Is there a solution?
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