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 and sound. Matrices are used in linear algebra to discuss systems of equations. The matrix itself is composed of the terms preceding each of the variables in each equation of the system. An example of a system of three equations would be: 2x + 3y + 4z, x +3y and 6x + 2y + 2z. The first row of the matrix for this system is [2 1 6], the second would be [3 3 2] and the third would be ....

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