Chapter 2.4 Determinants-Applications

Eigenvalues outline the classical adjoint a formula

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Unformatted text preview: Outline The Classical Adjoint A Formula for the Inverse of a Matrix Example Example Find the inverse of 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 Cramer’s Rule Theorem (Cramer’s Rule) If A is an invertible n × n matrix, the the unique solution of the system Ax = b is x = (x1 , x2 , . . . , xn ), where: xj = det(Ab,j ) det A (1 ≤ j ≤ n) and Ab,j is the n × n matrix obtained from A by replacing column j with b. Outline The Classical Adjoint A Formula for the Inverse of a Matrix Cramer’s Rule Eigenvalues The Proof Proof. The unique solu...
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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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