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Unformatted text preview: the following elementary matrices: E1 = In −2 0
01 , 001
E2 = 0 1 0 ,
100 1
0
E3 = 0
0 0
1
0
7 0
0
1
0 0
0 0
1 Outline Elementary Matrix Inverse of an Elementary Matrix The Inverse of a Matrix Elementary Matrices and Elementary Row Operations Theorem
If A is an m × n matrix and E is an elementary n × n matrix, then
EA is the m × n matrix obtained by performing the same
elementary row operation on A as required to obtain E from In .
Example
Demonstrate the 1
E = −2
0 theorem using: 00
1
2 −3
4
1 0 and A = 2 −1
0
3
01
2
2
1 −1 Outline Elementary Matrix Inverse of an Elementary Matrix The Inverse of a Matrix Inverse Elementary Matrix To each elementary row operation, there is an inverse
operation.
If an elementary row operation i...
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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.
 Spring '14
 KenyonJ.Platt
 Linear Algebra, Algebra, Matrices

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