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Beginning of Paper
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 sound we will need to define some essential terms. I am going to assume that a fair amount of Calculus is know to the reader in order to show ....

Middle of Paper
.... 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 matrix A subtracted from the product of the identity matrix and the variable lambda (Hughes-Hallet 90). The identity matrix is defined as a matrix with ones along it's diagonal and zeros everywhere else (Yaquib 23). Now having a rough idea of what the determinan ....

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