Hi all. I'm having a really tough time figuring out how to solve this problem:(adsbygoogle = window.adsbygoogle || []).push({});

Suppose that {v_{1}, v_{2}, v_{3}} are linearly independent vectors in R^{7}.

If

a_{1}= v_{1 }+ 2v_{2}

a_{2}= 3v_{2}– v_{3}

a_{3}= v_{1}– v_{2}+ v_{3},

determine directly from the definitions whether the vectors {a_{1}, a_{2}, a_{3}} are linearly independent or linearly dependent.

Can anyone help me? I know what linear dependence and linear independence are, and I know how to check for either using Gauss-Jordan elimination. But I'm not sure where to start on this problem.

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# Linear Independence/Dependence of Vectors

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