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I need to show whether or not the following statement is true:

For [tex]v_1,...,v_n\in Z^m[/tex], the set [tex]\{v_1,...,v_n\}[/tex] is linearly independent over Z [tex]\Leftrightarrow[/tex] it is linearly independent over R.

The reverse direction is true of course, but i'm having some trouble showing whether or not the forward direction is true. I'm pretty sure if R was replaced by Q, then the statement would be true, so the question boils down to irrational coefficients i think. I'm stuck at this point. Any thoughts?

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# Linear independence over Z

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