This paper devotes itself to the containment tracking problem of general linear time-varying discrete-time multi-agent systems (MASs). The convergence analysis is based on trajectory analysis rather than Lyapunov method. Nonnegative matrix theory, in particular the row-stochastic matrix properties, together with the relation between matrix and graph topology, are explored to handle the containment control problem. Based on a technical lemma concerning norm estimation of infinite product of row-stochastic matrices, we show that the followers can exponentially tend to the dynamical convex hull spanned by the leaders, i.e. the containment can be achieved under the very relaxed conditions: strictly instability of the individual-system of each agent (without interactions with other agents) is allowable and the graph topology is only required to be jointly having directed spanning forest frequently enough. Moreover, the least convergence rate is explicitly specified. Simulation is also provided to demonstrate the effectiveness of our result.