A family of nontrivial coefficients proves that the vectors are linearly dependent. Specifically, if you can find coefficients (not all zero) such that their linear combination with the vectors equals the zero vector, the set is dependent.
Conditions: You have a specific set of vectors.; You have found a parametric family of solutions to the homogeneous equation.; The parameter can be chosen to be nonzero.
A family of nontrivial coefficients proves that the vectors are linearly dependent. Specifically, if you can find coefficients (not all zero) such that their linear combination with the vectors equals the zero vector, the set is dependent.
Conditions: You have a specific set of vectors.; You have found a parametric family of solutions to the homogeneous equation.; The parameter can be chosen to be nonzero.