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TomLikesPhysics
 3 years ago
I need help with a matrix / Gauß.
TomLikesPhysics
 3 years ago
I need help with a matrix / Gauß.

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TomLikesPhysics
 3 years ago
Best ResponseYou've already chosen the best response.0I have no clue how one can get from the left matrix to the right matrix. To be more specific  I have no clue what I have to do to get the top line in right matrix.

TomLikesPhysics
 3 years ago
Best ResponseYou've already chosen the best response.0I totally get how I can get the middle and bottom line in the right matrix, but the one on top just seems wrong (the ratio).

TomLikesPhysics
 3 years ago
Best ResponseYou've already chosen the best response.0I just would like to know if the right matrix is right or if there must be a mistake.

phi
 3 years ago
Best ResponseYou've already chosen the best response.1Yes, it looks like a typo. You could get rid of the fractions If you multiply the 2nd row (after it is 0 1 2  0 ) by 8/5 and add to the top row you can get 1 2 3  0 for the top row but that does not match their row.

TomLikesPhysics
 3 years ago
Best ResponseYou've already chosen the best response.0I don´t know if this is important I am supposed to find the eigenvector but still I think I can not do some trick to get that row, right?

amistre64
 3 years ago
Best ResponseYou've already chosen the best response.01 2/5 1/5 0 18/5 36/5 ; 5/18 0 36/5 72/5 ; 5/36 1 2/5 1/5 0 1 2 0 1 2 ; this row is a multiple of the other 1 2/5 1/5 ; *5 0 1 2 0 0 0 5 2 1 0 1 2 0 0 0 i think it cant be turned

amistre64
 3 years ago
Best ResponseYou've already chosen the best response.0now if direction is what is important and not size, <5,0,0> = <1,0,0> but i cant verify that to be a good move

phi
 3 years ago
Best ResponseYou've already chosen the best response.1I'm sure it is a typo (somewheres). But exactly what are you trying to do here?

TomLikesPhysics
 3 years ago
Best ResponseYou've already chosen the best response.0Who are you talking to, phi? Me or amistre64? If you meant me. I was just trying to figure out if there is some way to rewrite the top line as it shown in the picture of if it is a typo. I thought it also might be a special case of operation that one can do because I am supposed to find the eigenvectors with this matrix so perhaps there is someway to get that top line because you can do stuff with this eigenstuff your normally can not do with a matrix.

phi
 3 years ago
Best ResponseYou've already chosen the best response.1I meant Tom. The reason I asked is that row operations do not preserve the eigenvalues (it would be nice if they did, because the eigenvalues sit on the diagonal of a triangular matrix) however, once you get an eigenvalue, you subtract it from the diagonal of the matrix and do gaussian elimination to find its corresponding eigenvector.

TomLikesPhysics
 3 years ago
Best ResponseYou've already chosen the best response.0That is what is happening here. The eigenvalue was 0 and I wanted to solve this matrix. The solution is the one above but because of the typo I was not sure I couldn´t follow it or if it simply was wrong. So, you are saying we can not multiply by five?

phi
 3 years ago
Best ResponseYou've already chosen the best response.1I tend to reduce the matrix all the way to reduced row echelon form starting with the original matrix on the left I get 1 0 1 0 1 2 0 0 0 now I read off the answer negate (1 2) and append a 1 to get (1 2 1) as the eigenvector

phi
 3 years ago
Best ResponseYou've already chosen the best response.1I got this from Strang's course http://ocw.mit.edu/courses/mathematics/1806linearalgebraspring2010/videolectures/lecture7solvingax0pivotvariablesspecialsolutions/ and maybe the following lecture

TomLikesPhysics
 3 years ago
Best ResponseYou've already chosen the best response.0Ok. Thanks a lot for your help phi. I saved my day. :)
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