Prove a set is linearly dependent

[algebrapro18]

Let T:Rⁿ->R^m be a linear transformation, and let {v₁,v₂,v₃} be a linearly dependent set in Rⁿ. Prove that the set {T(v1),T(v2),T(v3)} is Linearly Dependent.

PF:
Let T:Rⁿ->R^m be a linear transformation, and let {v₁,v₂,v₃} be a linearly dependent set in R^n.
Thenx₁v₁₊x₂v₂+x₃v₃ =0 has at least one nonzero x_i, call it x₁.
Since T is a linear transformation then T(x₁v₁)+T(x₂v₂)+T(x₃v₃) = x₁T(v₁)+x₂T(v₂)+x₃T(v₃)

Not really sure where to go from here.