In this paper, the linearizability of a [Formula: see text] resonant differential system is studied. First, we describe a method to compute the necessary conditions for linearizability based on blow-up transformation. Using the method, we compute necessary linearizability conditions for a family of [Formula: see text] resonant system with quadratic nonlinearities. The sufficiency of the obtained conditions is proven either by the Darboux linearization method or using the recursive procedure after blow-up transformation.

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