Generalization to Several Functions

The result of the above section is easily extensible to the general case in which the objective functional and equality constraints depend on several functions. 

If satisfying the above constraints I is optimum at y = y such that 

The constraint qualification yo 7 0 can be simplified by expanding the terms of the determinant. In general 

If a determinant is not zero, it means that its rows are linearly independent. In other words, none of the rows can be expressed as a linear combination of other rows. This result in case of the above determinant r o rneans that there is no Ki that can be expressed as a linear combination of other Kjy 

As a consequence, the simplified constraint qualification is that the vectors 

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