Gaussian Elimination is fucking HORSESHIT
how the fuck are you supposed to find the right way to go about solving the equation when all you're told is "Just multiply them and switch them around using the three rules bro" am i an absolute brainlet or is there really no actual step-by-step solution to this shit, it just seems like fucking guesswork when i got through the whole thing and the answer in the sheet was something completely fucking different.
WHAT THE FUCK AM I MISSING HERE?
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>mad engineer finally discovers he has to be creative and can't just plug and chug using memorized formulas
t. literal retard
Let's says you have an [math]n \times n[/math] matrix [math]A[/math] and want to solve the system
[eqn]A x = b [/eqn]
For [math]i [/math] from [math]1[/math] to [math]n-1 [/math] you do the following:
1) Look at the entries [math](a_{k,i})_{i \leq k \leq n} [/math] and find the index [math]j [/math] for which
[eqn]|a_{j,i}| = \max_{i \leq k \leq n} |a_{k,i}| [/eqn]
Then swap the i-th row with the j-th row.
2) For [math] k [/math] from [math] i+1 [/math] to [math] n [/math] add the i-th row multiplied by [math] -\frac{a_{k,i}}{a_{i,i}} [/math] to the k-th row.
That's literally it.
Haha yeah, fucking simple. You're just a brainlet OP kys.
When you have a single equation you know that you have to perform identical operations on both sides until the X stands alone and there's some sort of expression which doesn't contain X on the other side of the equals. Right?
In Gaussian elimination you want to get the coefficients along the diagonal (upper left to lower right) to all be equal to 1.
Start by making sure none of the diagonal elements is zero. Swap the top-to-bottom order of the equations if required to move the zero elsewhere. That is, the Nth term in equation N can't be zero. But a zero is OK in that column on any other line.
Now that the diagonal is all non-zeros, you want to make the diagonal values = 1. Say the first equation has a 3 in the first column and the second equation has a 5 in the first column. Multiply the second equation (all terms on both sides) by 2/5ths. Now the second equation has a 2 in the first column. Subtract it from the first equation. Now the first equation has a 1 on the diagonal.
Add (or subtract) another line from the second equation until line 2, column 2 = 1.
Continue until nothing remains but 1s on the diagonal.
The expressions on the right side (after the equals) are your answers.
That is: Each line is of the form; Ax1 + Bx2 + Cx3 = something
But on the first line A=1 and B and C are zero.
On the second line B=1 and A and C are zero.
And so on.
Worked example at en.wikipedia.org
Adding equations together allows to you isolate the coefficients. Gaussian elimination is just a systematic procedure for doing so.
I have no idea what this fucking nerd just wrote
am i supposed to start by turning the second one in the first collumn into a 0 or does it not matter which one i start with, i think that's what's fucking me up here. The 1 comes first and then the 0s below it right?
...
You can just solve each line one after another. It might not be the most elegant way for a particular matrix but you can do it.
It's just a systematic procedure.
Subtract lines from each other until all non-diagonal elements are zero.
If the diagonal elements aren't all 1, multiply until they are. e.g. If line 1 column 1 was 3, multiply the entire line by 1/3rd.
You don't HAVE carry out the operations in a specific order. But zeroing out all but the 1st column of the 1st line is a good way to start. Then zero out all but the 2nd column of the 2nd line, and so forth.
Following a fixed procedure minimizes the number of additions and multiplications you need to do.
Feel sorry for us old-timers who had to do it all with pencil and paper. You kids have it easy!
>oldfags migrated to Veeky Forums
makes sense
Just means that some of us can still multiply two digit numbers together without needing a calculator.
Most of the store clerks I see can't even make change without reading the display.
you're just stupid. that's all there is to it
>Gaussian Elimination is fucking HORSESHIT
>am i an absolute brainlet or is there really no actual step-by-step solution to this shit
But Gaussian elimination is extremely simple, what are you talking about?
... you know that those matrices represent equations, right?
I wish my linear algebra class actually involved solving equations. We had a proof based class, so it's all just memorizing rules and why they're true.
yeah, there is a trick/thing you're supposed to take advantage of
but i forget it lol
it might be that you have to start on the left side, then left and down one row, then left and down two rows until the end of the column, then the next column until it's diagonal
OP, are you clinically retarded?
Do more problems. You will eventually develop mental shortcuts.
Is this you OP?
it fucking matters which one you start with
Divide top row so that leftmost entry equals 1. If it's already zero shuffle the rows that it's not.
Then subtract top row from all the other rows so as to make the left column zero, except from the 1 at the top from the first step.
Keep going. Christ thats literally all there is to it.
:^)
>he thinks Gauss is bad
OP let me tell you about Recurrence Equations and the extended Euclidean Algorithm.
this is literally the easiest thing in linear algebra you absolute fuck
>dividing and reminder simple manipulation is hard
why am i even wasting my time here jesus christ
is this a joke?
the abstract part of linear algebra is the worst. idk if I've just had shit profs or what but I don't fuckin get it
>am i an absolute brainlet
yeah
yes
isn't that some algebra 2 memeing
just look up a video on Gauss Jordian elimination
Protip:If you skin color is black or you don't have a penis you might as well drop out
you're a nigger
you can conduct gaussian elimination with a completely brainless algorithm
think about it. first step is multiply row 1 by the inverse of the first coefficient, turning it to 1.
then, multiply that by the negation of the second coefficient and add it to the second row, which turns its first coefficient to 0. then repeat from the second coeffeciient.
it's SO EASY, even a MINDLESS computer can do it.
matrix.reshish.com
you are black, right?
drop out of your program, NOW.
>Protip:If you skin color is black or you don't have a penis you might as well drop out
My guess is both tbqh
Just look up a proof bro
>I have no idea
... bcoz:
I feel like I almost understand this, user could you write this in pseudo code?
you're a fucking brainlet that is like one of the simplest algos
Yes, you are just retarded.
I knew how to do it before even being taught "Gaussian Elimination", just by know how to solve simple 2x2 linear systems in highschool.