(100), (11-1),(1-11) the associated matrix is defined as the coordinates of the transformed vector (im(f)) the base, as we're in the canonical base, we obtain one, and we see how it works... the coordinates of (100) in the canonical base are three coeficients: one alpha multiplying (100), one beta multiplying(010) and one gamma multiplying (001) in order to get the transformed vector, as we see, the coordinates are always the components of the vector, in the canonical base so the associated matrix will result as the components of the transformed vector displayed in columns and we get the associated matrix with respect to the canoncal base of the linear application 