We consider operators on the matrix-valued disc algebra. We show that any bounded linear operator T: A[otimes ][Kscr ]→X to a Banach space X of cotype 2 induces a bounded operator Gν→X defined on some weighted Bergman space Gν on the unit disc. We give sufficient conditions on the weight ν for the formal inclusion A[otimes ][Kscr ]→Gν to be 2−C*-summing. Decompositions of T with respect to operator-valued measures are obtained.