Consider a linear transformation T:R → R² defined by

  T = (x, 3x); x ∈ R

To find matrix associated with T w.r.t given bases of real vector spaces R and R².

Choose

  B₁ = {} as a basis of R and
  B₂ = {(, ) , (, )} as a basis of R²

NOTE: You can observe that different bases may give different matrices.