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 />
⎡<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 />
⎡ x<br />
x<br />
⎢⎢⎢<br />
⎣x<br />
1<br />
2<br />
3<br />
⎤<br />
⎥⎥⎥<br />
⎦<br />
=<br />
⎡<br />
⎢⎢⎢<br />
⎣−<br />
36⎤<br />
7<br />
31⎥⎥⎥<br />
⎦<br />
[A][x] = [B]<br />
[x] = [A] -1 [B]<br />
⎡ x<br />
x<br />
⎢⎢⎢<br />
⎣x<br />
1<br />
2<br />
3<br />
⎤<br />
⎥⎥⎥<br />
⎦<br />
=<br />
⎡<br />
−<br />
⎢⎢⎢<br />
⎣<br />
2<br />
3<br />
5<br />
− 4<br />
5<br />
3<br />
5<br />
7<br />
− 8<br />
⎤<br />
⎥⎥⎥<br />
⎦<br />
−1<br />
⎡ 36⎤<br />
7<br />
⎢⎢⎢<br />
⎣−<br />
31⎥⎥⎥<br />
⎦<br />
The division of two matrices is not defined in<br />
linear algebra, however, matrix inversion can<br />
be used much the same way division is used to<br />
solve a matrix equation.<br />
A matrix can be inverted if it is a nonsingular<br />
matrix. Meaning:<br />
D [ A] ≠ 0<br />
Overhead 2 of 16
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