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[itex]e_1^ e_2 + e_3^e_4[/itex] is not decomposable when the dimension of the vector space is greater than 3 and e_i are basis vectors.

I solved it by mounting a set of 6 equations with 8 unknows and studying the different posibilities cheking that each one is not solvable.

Is there any nicer way to tackle this problem? if so please let me know