Matrix Inversion by Gauss-Jordan Elimination
Matrix Inversion by Gauss-Jordan Elimination
Matrix Inversion by Gauss-Jordan Elimination
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GE 120 Lecture overheads<br />
We can actually perform the row operations<br />
on both [A] and [I] at the same time.<br />
⎡<br />
−<br />
⎢⎢⎢<br />
⎣<br />
2<br />
3<br />
5<br />
−<br />
4<br />
5<br />
3<br />
5<br />
7<br />
− 8<br />
⎤<br />
⎥⎥⎥<br />
⎦<br />
⎡1<br />
0<br />
⎢⎢⎢<br />
⎣0<br />
0<br />
1<br />
0<br />
0⎤<br />
0<br />
1⎥⎥⎥<br />
⎦<br />
R′<br />
2<br />
R′<br />
3<br />
→<br />
3<br />
2<br />
→ −<br />
R<br />
5<br />
2<br />
1<br />
R<br />
+<br />
1<br />
R<br />
+<br />
2<br />
R<br />
3<br />
⎡2<br />
0<br />
⎢⎢⎢<br />
⎣0<br />
− 4<br />
− 1<br />
13<br />
29<br />
− 41<br />
5<br />
2<br />
2<br />
⎤<br />
⎥⎥⎥<br />
⎦<br />
⎡<br />
⎢⎢⎢<br />
⎣−<br />
3<br />
5<br />
1<br />
2<br />
2<br />
0<br />
1<br />
0<br />
0⎤<br />
0<br />
1⎥⎥⎥<br />
⎦<br />
Overhead 4 of 16
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