# Lec3_45 - NOTES ON SECTION 3.4 AND 3.5 MA265 Key words Inverse Adjoint(or adjugate Cramers rule 1 Inverse using determinants The point of 3.4 is a

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NOTES ON SECTION 3 . 4 AND 3 . 5 MA265, SECTIONS 41, 52 Key words Inverse Adjoint (or adjugate) Cramer’s rule 1. Inverse using determinants ‘ The point of 3 . 4 is a purely algebraic (but very complicated) expression for the inverse of a matrix. In words, the inverse of a matrix A is the adjoint matrix (this terminology is unfortunate for reasons we will not explain – wikipedia prefers the name “adjugate matrix”, as would I) scaled by 1 / det A . The adjoint matrix, in turn, is the transpose of the matrix of cofactors. That is Deﬁnition 1. The adjoint matrix of the matrix A is the matrix adj A = A 11 A 21 ... A n 1 A 12 A 22 ... A n 2 . . . . . . . . . A 1 n A 2 n A nn where the A ij are the cofactors of the entries a ij of the matrix A . Remark 2. Note carefully the strange ordering of the entries!!! It is the transpose of what you would write if you simply replaced the entries of the matrix with its cofactor. As I was saying,

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## This note was uploaded on 03/31/2012 for the course MA 265 taught by Professor Bens during the Spring '08 term at Purdue University-West Lafayette.

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Lec3_45 - NOTES ON SECTION 3.4 AND 3.5 MA265 Key words Inverse Adjoint(or adjugate Cramers rule 1 Inverse using determinants The point of 3.4 is a

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