Find the value of k, a constant so that the 3x3 system has a unique solution

Brief explanation of how to find the value of k, that is to say a constant or parameter so that the system has a unique solution, that is to say it is compatible determined. In this exercise it was developed using the Gaussian method to develop the non-homogeneous system of linear equations with 3 unknowns expressed in the 3x3 matrix form.
In other cases, this Linear Algebra exercise is similar to finding the value of k so that the system has a unique solution.

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