Work out linear independence instantly with clear inputs, formula shown and shareable results.
Vectors are linearly independent when the only combination giving zero is the trivial one. That happens exactly when the rank equals the number of vectors, or equivalently when a square arrangement has non-zero determinant.
Independence test
independent ⇔ rank = number of vectors ⇔ det ≠ 0 for a square set
The third is the sum of the first two, so the rank is 2 and they are dependent.
No. Any set of more than n vectors in n-dimensional space is necessarily dependent.