Matrix Inversion by Gauss-Jordan Elimination
Matrix Inversion by Gauss-Jordan Elimination
Matrix Inversion by Gauss-Jordan Elimination
Create successful ePaper yourself
Turn your PDF publications into a flip-book with our unique Google optimized e-Paper software.
GE 120 Lecture overheads<br />
⎡ x<br />
x<br />
⎢⎢⎢<br />
⎣x<br />
1<br />
2<br />
3<br />
⎤<br />
⎥⎥⎥<br />
⎦<br />
⎡<br />
= −<br />
⎢⎢⎢<br />
⎣<br />
0.176<br />
0.036<br />
0.101<br />
0.042<br />
0.117<br />
0.077<br />
0.159⎤⎡<br />
36 ⎤<br />
0.087 7<br />
0.006⎥⎥⎥<br />
⎦⎢⎢⎢<br />
⎣−<br />
31⎥⎥⎥<br />
⎦<br />
x1 = 0.176 × 36 + 0.042 × 7 + 0.159 × ( −31)<br />
=<br />
1.701<br />
x2 = −0.036<br />
× 36 + 0.117 × 7 + 0.087 × ( −31)<br />
= −3.174<br />
x3 = 0.101 × 36 + 0.077 × 7 + 0.006 × ( −31)<br />
=<br />
3.989<br />
Compare the two solutions:<br />
Elements as fractions<br />
x 1 = 2<br />
x 2 = -3<br />
x 3 = 4<br />
Elements as decimals<br />
x 1 = 1.701<br />
x 2 = -3.174<br />
x 3 = 3.989<br />
Why are the two solutions different?<br />
Overhead 16 of 16
Change language