Chapter 2.4 Determinants-Applications

Chapter 2.4 Determinants-Applications

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Unformatted text preview: cofactor of A at aij is the number Cij = (−1)i +j |Aij |. Definition The matrix C = [Cij ] is called the matrix of cofactors of A. The matrix adj(A) = C T is called the classical adjoint of A. Outline The Classical Adjoint A Formula for the Inverse of a Matrix Example Example Find the classical adjoint of the matrix 100 A= 2 3 0 456 Cramer’s Rule Eigenvalues Outline The Classical Adjoint A Formula for the Inverse of a Matrix Cramer’s Rule Eigenvalues A Preliminary Result Theorem Suppose A = [aij ] is an n × n matrix with cofactor Cij at aij . Then for any 1 ≤ i , j ≤ n, n det A if i = j 0 if i = j aik Cjk = k =1 Proof. If i = j , then the sum is det A. If...
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This note was uploaded on 02/10/2014 for the course MATH 2270 taught by Professor Kenyonj.platt during the Spring '14 term at Snow College.

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