lienar algebra

[Guest]

I can't figure this out, I don't think it should be that hard though

Show that if v1, v2, ...vn is a linearly independent set of vectors, then any subset of thses vectors is also linearly independent.

any ideas?
Thanks
Ben

 

[pka]

Here is the basic idea.
Because \(\displaystyle \{ v_1 ,v_2 ,v_3 ,...v_n \}\) is a linearly independent set of vectors not non-trivial linear combination of these vectors equals the zero vector.

Well just suppose the for example \(\displaystyle \alpha v_1 + \beta v_2 = O\quad \alpha \not= 0\quad \& \quad \beta \not= 0.\)
If that were the case then \(\displaystyle \alpha v_1 + \beta v_2 + 0v_3 + ... + 0v_n = O\) which is a contradiction to the given.

 

[Guest]

thanks a lot - couldn't think of how to prove it correctly, i appreciate it