# gaussian elimination -- pivoting

• Dec 8th 2010, 08:45 AM
rlkmg
gaussian elimination -- pivoting
1. I dont really understand how my lecture notes got the answer when doing full pivoting? I thought i can just interchange column 1 and 3?
http://img560.imageshack.us/img560/4238/59122878.jpg

2. What does it mean by: "when swapping columns, must swap results?"
http://img401.imageshack.us/img401/9728/90750707.jpg

3. When doing full pivoting, is my matrice correct (to start guassian elimination)?
http://img444.imageshack.us/img444/1244/67037046.jpg

Thanks, and most appreciated.
• Dec 8th 2010, 09:47 AM
Ackbeet
Elementary row operations do not change the solution space (and/or kernel) of a matrix, but they do change the image. Conversely, elementary column operations do not change the image, but they do change the solution space. So, if you are trying to solve a linear system, you have to keep track of how your elementary column operations are changing the solution space.
• Dec 8th 2010, 11:15 AM
rlkmg
thanks, how would i swap the results?
• Dec 8th 2010, 11:17 AM
rlkmg
thanks, how would i swap the results?
• Dec 8th 2010, 01:05 PM
Ackbeet
Ok, let's say you have the system Ax = b, where x = (x1, x2, x3). Let's say that in matrix A you swap columns 1 and 3. Then the new system will have solutions (x3, x2, x1). That is, you swap the corresponding variables. Make sense?