The main purpose of this paper is to introduce the necessary and sufficient conditions for the matrix of interval numbers Ā = (ānk) such that Ā-transform of x = (xk) belongs to the sets c0S(i) ∩ ℓi∞, cS(i) ∩ ℓi∞, where in particular x ∈ c0S(i) ∩ ℓi∞ and x ∈ cS(i) ∩ ℓi∞ respectively.