Determine which of the sets of vectors Is linearly independe

Determine which of the sets of vectors Is linearly independent. A: The set {P1,P2,P3} where p1(t) = 1, P2(t) = t^2, P3(t) = 3 + 3t B: The set {p1,p2,P3} where P1(t) = t, P2(t) = t^2, P3(t) = 2t + 3t^2 C: The set {p1,p2,p3} where P1(t) = 1, P2(t) = t^2, P3(t) = 3 + 3t + t^2 B only A and C all of them A only C only

Solution

in A and C , P₃ can not be written as combination of P₁ and P₂

so they are linearly independent