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Chapter 2.4 Determinants-Applications

Chapter 2.4 Determinants-Applications - Outline The...

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Outline The Classical Adjoint A Formula for the Inverse of a Matrix Cramer’s Rule Eigenvalues Applications of the Determinant Math 2270 K. J. Platt, Ph.D. Department of Mathematics Snow College Spring 2014
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Outline The Classical Adjoint A Formula for the Inverse of a Matrix Cramer’s Rule Eigenvalues Outline 1 Classical Adjoint 2 Formula for the Inverse 3 Cramer’s Rule 4 Eigenvalues
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Outline The Classical Adjoint A Formula for the Inverse of a Matrix Cramer’s Rule Eigenvalues Non-Additivity of the Determinant Suppose A = [ a ij ] is an n × n matrix. Recall that A ij is the ( n - 1) × ( n - 1) matrix obtained from A by deleting its i th row and j th column. The cofactor of A at a ij is the number C ij = ( - 1) i + j | A ij | . Definition The matrix C = [ C ij ] is called the matrix of cofactors of A . The matrix adj ( A ) = C T is called the classical adjoint of A .
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Outline The Classical Adjoint A Formula for the Inverse of a Matrix Cramer’s Rule Eigenvalues Example Example Find the classical adjoint of the matrix A = 1 0 0 2 3 0 4 5 6
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