How To Perform Gauss Elimination | Numerical Methods

[@spoperty4940]

This explenation is comically bad, even the wikipedia explenation is better... Here is a good explanation for anyone that is already here and was just as confused: We use the fact that ax+by+cz+...= some constant, and then we look at the other equations and try to make every number "below" the diagonal a zero, so we look for example at the equation 2x +y -z=8, and we notice that our second equation, which is -3x-y+2z=-11, needs to get rid of the x component, so we check how many E1(E1,E2, E3,... are the 1st 2nd and 3rd equation and so on) do we need to make the coeficient of E2's "x" disappear, so we do -3+m*(2)=0 (we are checking how many 2's we need to reset it), so we see we need to add E1 to E2 3/2 times, we do that and we get 0x+y/2+z/2=?, how do we find this constant E2 equals, well we use the fact that E1=8 and that we added (3/2)E1 so it's like we added 8*(3/2) to our constant -11. so now we are 1 step closer to getting to our triangular form!, we can do the same thing on E3 which is -2x +y +2z=-3, i'll leave it as an exercise to see if you understand what is going to be our new E3 after killing the x component, and now we need to modify E3 again, because we want E3 to only have a z component(for our triangle), we see that adding E1 is useless as we will go back to having an x(we don't want this), so we use E2, again I'll leave as an exercise to see if you undertstand, finally we reach a easily solvable system of equations, we see from E3 that z=-1, then we go back to E2 with our E3 result and see that y=3, and then we go back to E1 equipped with y and z and we solve it simply for our point being (x=2, y=3, z=-1). this example is from the wiki article with a comprehensive hand holding solution steps by me. en.wikipedia.org/wiki/Gaussian_elimination, this might also be a little hard to understand but i promise looking at the table on wikipedia for a few minutes will make you understand.

[@wateriswetloser]

Its a 4 minute long explanation, calm down lol, way shorter than how long itd be taught at a university

[@alexb3613]

kzbin.info/www/bejne/qZbIpWyMrq2iabM

[@almikntolkein7489]

Gaussian elimination are of two types one is upper triangular form and other is row echolon form, right?

[@AsasinHD]

hi, nice video, but don't you have any video of this in python?

[@StudySessionYT]

Not currently, however, I plan on creating this video in the near future!

[@Quarbenah_Fendi]

Please I had different answers x=1/5, y=-2/5, z=11/5. Please should the answers ne different when you try to use any other method?

[@pholmarlon2537]

same answer with mine

[@Quarbenah_Fendi]

@@pholmarlon2537 I hope it helped though?

[@alexb3613]

kzbin.info/www/bejne/qZbIpWyMrq2iabM

[@christianarbalate2361]

it's just the same, the only difference is that your answer is express in lowest term while his answer is not.

[@is_adjekofori]

He made a mistake. The first equation according to his explanation should be Z (15/2) = 33/2 Making z = 11/5

[@DJosh-cs5vx]

Thanks

[@hannatorres6913]

What???

[@rexallassani2321]

ikr🥲

[@alexb3613]

kzbin.info/www/bejne/qZbIpWyMrq2iabM