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 />
Overhead 10 of 16<br />
⎥⎥⎥<br />
⎦<br />
⎤<br />
⎢⎢⎢<br />
⎣<br />
⎡<br />
−<br />
−<br />
⎥⎥⎥<br />
⎦<br />
⎤<br />
⎢⎢⎢<br />
⎣<br />
⎡<br />
−<br />
168<br />
1<br />
168<br />
13<br />
168<br />
17<br />
336<br />
29<br />
336<br />
41<br />
336<br />
11<br />
168<br />
53<br />
168<br />
17<br />
168<br />
61<br />
1<br />
0<br />
0<br />
0<br />
1<br />
0<br />
0<br />
0<br />
2<br />
2<br />
2<br />
1<br />
1<br />
2<br />
1<br />
R<br />
R<br />
R<br />
R<br />
→ −<br />
′<br />
→<br />
′<br />
⎥⎥⎥<br />
⎦<br />
⎤<br />
⎢⎢⎢<br />
⎣<br />
⎡<br />
−<br />
⎥⎥⎥<br />
⎦<br />
⎤<br />
⎢⎢⎢<br />
⎣<br />
⎡<br />
168<br />
1<br />
168<br />
13<br />
168<br />
17<br />
336<br />
29<br />
336<br />
41<br />
336<br />
11<br />
336<br />
53<br />
336<br />
17<br />
336<br />
61<br />
1<br />
0<br />
0<br />
0<br />
1<br />
0<br />
0<br />
0<br />
1<br />
Therefore<br />
[ ]<br />
⎥⎥⎥<br />
⎦<br />
⎤<br />
⎢⎢⎢<br />
⎣<br />
⎡<br />
−<br />
=<br />
−<br />
168<br />
1<br />
168<br />
13<br />
168<br />
17<br />
336<br />
29<br />
336<br />
41<br />
336<br />
11<br />
336<br />
53<br />
336<br />
17<br />
336<br />
61<br />
A 1