We derive bounds for the solution of an irreducible tridiagonal linear system of dimension N which arises in many areas of numerical analysis. The conditions for which the linear system is invertible and its solution bounded by a constant independent of N or dependent weakly on N are established. The results derived are strictly related to the study of the condition number for the coefficient matrix of the system. Two examples which lead to this kind of linear systems are given, the second of which derives from the solution of boundary value problems by means of difference methods
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