Elementary Matrices
Elementary Matrices
Elementary Matrices
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Left Multiplication by E<br />
Theorem<br />
If E is an elementary matrix obtained from Im by performing a<br />
certain elementary row operation and if A is an m × n matrix<br />
then EA is the matrix that results from performing the same<br />
elementary row operation on A.<br />
Example<br />
Let A =<br />
E2 =<br />
⎡<br />
⎣<br />
⎡<br />
⎣<br />
1 2 3<br />
4 5 6<br />
7 8 9<br />
1 1 0<br />
0 1 0<br />
0 0 1<br />
and calculate E1A, E2A, and E3A.<br />
⎤<br />
⎡<br />
⎦ , E1 = ⎣<br />
⎤<br />
⎡<br />
⎦ , E3 = ⎣<br />
J. Robert Buchanan <strong>Elementary</strong> <strong>Matrices</strong><br />
1 0 0<br />
0 2 0<br />
0 0 1<br />
1 0 0<br />
0 0 1<br />
0 1 0<br />
⎤<br />
⎦ ,<br />
⎤<br />
⎦ ,
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