what to do for this one:

Given: 3 vectors,a,b,c, are linearly independent in a vector space V

Asked: Show that 3a, 2a-b,a+care also linearly independent

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- Oct 22nd 2009, 05:15 PMNoxide[SOLVED] I don't know
what to do for this one:

Given: 3 vectors,**a**,**b**,**c**, are linearly independent in a vector space V

Asked: Show that 3**a**, 2**a**-**b**,**a**+**c**are also linearly independent - Oct 22nd 2009, 05:29 PMDefunkt
Assume 3a, 2a-b, a+c are dependent. Then, there exist scalras , not all zero, such that

If then . Therefore not all the coefficients are zero.

Let

Then but not all of the coefficients are zero, in contradiction to the fact that a,b,c are linearly independent... ==> the assumption can not hold, therefore 3a, 2a-b and a+c are linearly independent. - Oct 22nd 2009, 05:51 PMNoxide
wow, that's a really awesome proof by contradiction!

thanks for the help (Clapping)