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What are the Cramer’s solutions equated to while using Cramer’s method of classifying a PDE?

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What are the Cramer’s solutions equated to while using Cramer’s method of classifying a PDE?

(a) The dependent variables

(b) The derivatives of dependent variables

(c) The second derivatives of dependent variables

(d) The highest derivatives of dependent variables

This question was addressed to me during an online exam.

The above asked question is from Classification of PDE in section Mathematical Behaviour of Partial Differential Equations of Computational Fluid Dynamics

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Right option is (b) The derivatives of dependent variables

The explanation is: For characteristic lines, the derivatives of dependent variables are zero. Cramer’s rule is used to find these derivatives and then it is made indeterminate to find the type of PDE.

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