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Mark44
#3
Mar10-11, 03:52 PM
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P: 21,294
You are given that the set {v1, v2, ..., vn} is linearly independent, which means that the equation
c1v1 + c2v2 + ... + cnvn = 0 has only the trivial solution.

Now look at the equation a1(v1 - b) + a2(v2 - b) + ... + an(vn - b) = 0, where b != 0, and b != vi, and show that this equation has only the trivial solution.