Linear Dependence can be proved if the Linear Combination of Vectors equate to zero without having all the Coefficients of the Vectors as zero.
$ c1V1 + c2V2 + …. + cnVn = 0 $, where at least one ci ! = 0
i.e. Let c1 != 0, then : $V1 = – (\frac{c2}{c1}V2 + \frac{c3}{c1}V3 + ... + \frac{cn}{c1}Vn )$ => L.D
Since u, v, w can already be written as Option A or Option B to prove L.D, Option C violates the above rule.
Option D: LHS ! = RHS as 7u – 1v + 1w = 2v and not 0.
Therefore, Option A,B are correct