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 + c are also linearly independent
If then . Therefore not all the coefficients are zero.
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.