In the framework of the Mims transformation matrix method the equations for the nuclear magnetizations are obtained which describe the dynamics of nuclear spin-systems with strong Larmor and Rabi inhomogeneous broadenings of the NMR line in conditions of their nonequilibrium which were earlier obtained by the statistical tensors method. As an example, the properties of the proton single-pulse echo and its secondary signals in a test material (silicone oil) coated on the surface of high-<$E T sub c> superconducting-oxide powders and in metallic hydride are presented.

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