73 is that speeds and more generally rates are

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Unformatted text preview: ltiple of another row moving from one matrix to the next. Furthermore, since C is upper triangular, det(C ) is the product of the entries on the main diagonal, in this case det(C ) = (3)(−1) 133 = −13. This demonstrates the utility of using row operations to assist in calculating determinants. This also sheds some light on the connection between a determinant and invertibility. Recall from Section 8.4 that in order to find A−1 , we attempt to transform A to In using row operations A In Gauss Jordan Elimination −− − − − − − −→ −−−−−−−− I n A− 1 As we apply our allowable row operations on A to put it into reduced row echelon form, the determinant of the intermediate matrices can vary from the determinant of A by at most a nonzero multiple. This means that if det(A) = 0, then the determinant of A’s reduced row echelon form must also be nonzero, which, according to Definition 8.4 means that all the main diagonal entries on A’s reduced row echelon form mus...
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