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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 whether or not this argument is valid an ....

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 determinant and eigenvalues a ....

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