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Week 3: Matrix Inverse, Elementary Matrices, and Inverse Properties

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Introduces elementary matrices, row swapping, and row addition. Explains how to construct a product of elementary matrices to represent a sequence of row operations. Discusses matrix inverses, including how to compute them. Invertibility of elementary matrices, the behavior of inverses under transposition and multiplication, and conditions for a matrix to be invertible based on its row-reduced echelon form (RREF).

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Uploaded on
May 27, 2025
Number of pages
3
Written in
2024/2025
Type
Class notes
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week 3 Video
Elementary Matrices
Example suppose a is a 3in matrix

a find a 3 3 matrix E suchthat E A is the resultof multiplying R2 by 5

so E

8 E suchthat EZA is theresultof exchanging RaandRs of A
21
p
Es suchthat ESA isresultofreplacingRaof Awith 5times r addedto ra



p p
d find a 3 3 matrix M so that mA resultsafterpreforming a b and c
sol M E E E

Hill ill
Hill




2.1.7 2.1.8 pg 11 78
2.1.92.1.10 pg7890
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