Final answer:
The matrix method includes the creation of a matrix of partial derivatives and finding eigenvalues; it applies to implicit functions and is used in multivariable calculus, going beyond the simple mathematical principles of inverting a function.
Step-by-step explanation:
The student's question pertains to the matrix method in the context of implicit functions and multivariable calculus. The matrix method they refer to is likely about the Jacobian matrix in multivariable calculus, which is a matrix of partial derivatives and is used to study the behavior of multivariable functions. This method involves creating a matrix that encapsulates the linear approximation to a function at a given point and can involve finding eigenvalues to analyze specific properties like stability. It's crucial to understand that mathematics starts with simple concepts, such as inverting a function, as in finding the side length 'a' from the equation a2 = c2 - b2 using the Pythagorean theorem in algebra, and builds up to more complex topics such as calculus and multivariable calculus.
An eigenvalue is a concept from linear algebra applied in various branches of calculus, including multivariable calculus, not just implicitly. It is wrong to say that the matrix method is used only in multivariable calculus, as it's also fundamental in linear algebra and in the analysis of linear systems in various contexts.