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Cramer - ME 210 Applied Mathematics for Mechanical...

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ME 210 Applied Mathematics for Mechanical Engineers Prof. Dr. Faruk Arınç Spring 2010 Cramer’s Rule A useful application of determinants to the solution of linear algebraic equations [A] [x] = [b] is the Cramer’s rule , which can be used only when the coefficient matrix [A] is a non-singular and square matrix. Note that when [A] is a nonsingular matrix, it has a nonzero determinant (that is, det[A] ≠ 0, hence its rank is full (that is rank[A] = n), hence rank[A] = rank[A¦b], thereby the solution exists and is unique .
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