Determine which of the sets of vectors is linearly independe

Determine which of the sets of vectors is linearly independent. The set { p1,p2,p3} where p1(t) = 1, p2(t) = t^2 p3(t) = 3t + 4t + 2 The set { p1,p2,p3} where p2(t0 = t, p2(t) = t^2, p3(t) = 3t + 4t = t^2 The set {p1,p2,p3} where p1(t) = 1, p2(t) = t2, p3(t) = 3t + t4 = t^2.

Solution

A set of vectors is linearly independent if no vector in the set is (a) a scalar multiple of another vector in the set or (b) a linear combination of other vectors in the set

since all sets A,B,AND C follows above criteria all sets of vectors is linearly independent.