I understand that first you have to prove that it's linearly independent, but wouldn't a coefficient of 0 always work?
Ex:
$a_1(u+v+w) + a_2(-2u+v-w) = 0$ For any vector, wouldn't $a_1 = a_2 = 0$ always hold?
2026-03-25 01:35:25.1774402525
Finding a Basis of a Vector Space - Coefficients
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Yes, it holds and hence we call it the trivial solution.
What is of interest is to examine if there is any non-trivial solution. If there is only the trivial solution, it is linearly independent. Otherwise, it is linearly dependent.