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Math Help - show columns are linearly independent if homogeneous system has only trivial solution

  1. #1
    Member Jskid's Avatar
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    show columns are linearly independent if homogeneous system has only trivial solution

    Let A be an m x n matrix. Show that the columns of A are linearly independent iff the homogeneous system Ax=0 has just the trivial solution.

    I think I need to use the fact that a homogeneous system of n linear equations in n unknowns has a nontrivial solution iff rank(A) < n
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  2. #2
    MHF Contributor FernandoRevilla's Avatar
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    You only need to express the system Ax=0 in the form x_1C_1+\ldots+x_nC_n=0 and apply the definitions of linearly independence and solution of a system.
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