Let be the Lie algebra of the semi-direct sum of the real vector space and the Lie algebra of the sets of all real matrices. In this paper, a Frobenius functional is constructed in order for the Lie algebra to be the real Frobenius Lie algebra of dimension 8. Moreover, a bilinear form corresponding to this Frobenius functional is symplectic. Then the obtained symplectic bilinear form induces the left-symmetric algebra structures on . In other words, the Lie algebra is the left-symmetric

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... In particular, we give the formulas of its left-symmetric algebra structure explicitely. The left-symmetric algebra structures for case of higher dimension of this Lie algebra type are still an open problem to be investigated.