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 />
Instead of carrying the matrix elements as<br />
fractions during the row transformations we<br />
may carry the elements as decimal numbers.<br />
⎡<br />
−<br />
⎢⎢⎢<br />
⎣<br />
2<br />
3<br />
5<br />
−<br />
4<br />
5<br />
3<br />
−<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 />
3<br />
→ R1<br />
+ R2<br />
2<br />
5<br />
→ − R1<br />
+ R<br />
2<br />
3<br />
⎡2<br />
0<br />
⎢⎢⎢<br />
⎣0<br />
− 4<br />
− 1<br />
13<br />
−<br />
5<br />
14.5<br />
20.5<br />
⎤<br />
⎥⎥⎥<br />
⎦<br />
⎡ 1<br />
1.5<br />
⎢⎢⎢<br />
⎣−<br />
2.5<br />
0<br />
1<br />
0<br />
0⎤<br />
0<br />
1⎥⎥⎥<br />
⎦<br />
R ′ →<br />
3<br />
1 R<br />
13<br />
3<br />
⎡2<br />
0<br />
⎢⎢⎢<br />
⎣0<br />
− 4<br />
− 1<br />
1<br />
5<br />
14.5<br />
− 1.577<br />
⎤<br />
⎥⎥⎥<br />
⎦<br />
⎡<br />
⎢⎢⎢<br />
⎣−<br />
1<br />
1.5<br />
0.192<br />
0<br />
1<br />
0<br />
0⎤<br />
0<br />
0.077⎥⎥⎥<br />
⎦<br />
Overhead 12 of 16
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