A set of vectors is linearly independent exactly when the only linear combination that equals the zero vector forces all coefficients to be zero. If there exists a nontrivial coefficient choice (at least one coefficient is nonzero) that produces the zero vector, the set is linearly dependent.
Conditions: The context is a set of vectors in a vector space.; We are testing for linear independence or dependence.
A set of vectors is linearly independent exactly when the only linear combination that equals the zero vector forces all coefficients to be zero. If there exists a nontrivial coefficient choice (at least one coefficient is nonzero) that produces the zero vector, the set is linearly dependent.
Conditions: The context is a set of vectors in a vector space.; We are testing for linear independence or dependence.