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

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
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,
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

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.

Page1 / 2

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

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online