Beginning of Essay
An argument given by professor Loren Johnson of the Mathematics Department of the University of California Santa Barbara states: The determinant of the n x n matrix A is the product of it's eigenvalues (Yaquib 303). In order to show if this argument is valid and s ....

Middle of Essay
.... n represent the number of rows and columns. The signed elementary products of A can be defined as 1 when the permutation of the elementary products is even and -1 when the permutation of the elementary products is odd (Hughes-Hallet 20). These two numbers are then multiplied by their respective permutation and the whole lot is added together. When all calculations are said and done this results in a number for matrix A, in this case -58. This now leads us to the definition of an eigenvalue. Since we have already defined A as a n x n matrix we can say that the eigenvalues are the solutions of the equation obtained from taking the determinant of the mat ....