Part IV: Matrix Algebra

This part of the course extends the concept of inverse functions to the case where y = f(x) with y = (y1, y2, …, yn) and x = (x1, x2, …, xn). In more user-friendly terms this part asks us to determine when and how the system of equations that expresses y1, y2, … and yn as functions of x1, x2, and xn can be “inverted” to express x1, x2, and xn as functions of y1, y2, … and yn . This motivates the study of matrix algebra since the process of inverting an n x n square matrix is used to show how we decide whether a function f(x1, x2, …, xn) has an inverse and how we find the inverse function if it exists.

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