linearly independent

[korean]

question: If a set contains fewer vectors than there are entries in the vectors, then the set is linearly independent? ex. M*N matrix where M>N

**i cant make up my mind! i know if you have more vectors than there are entries, then the set is linearly dependent because you have a free varible.**

my first guess is no but i cant find a reason or justification for it. everytime i think about it i start to think yes.

please someone help me understand or point me in the right direction or give me a very good explaination of it.

thanks.

 

[pka]

In \(\displaystyle \Re ^3\) consider the set of vectors \(\displaystyle \left\{ {\left\langle {1,2,0} \right\rangle ,\left\langle { - 1, - 2,0} \right\rangle } \right\}\).
Is that a linearly independent set?

 

[korean]

thank you! i understand now