Explain this sheet like im 5 year old idiot female only child

[analog canyon]

Wth is gauss

Explain this sheet like im 5 year old idiot

[knotty nexus]

Waitbwhat

[analog canyon]

Explain this sheet like im 5 year old idiot female only child

[knotty nexus]

Hila

Hola

Im new

[sharp storm]

Do you know whats an augmented matrix ?

[knotty nexus]

Absolutely no clue

Wait matrix is like

Where theres uh numbers in a 3x3 position

[sharp storm]

Yeah

It looks like a tab of number

[knotty nexus]

Wait whats gauss and gauss jordan

Right

[sharp storm]

An algorithm on rows to make it triangular

[knotty nexus]

Uh idk what that means

Would u mind if tell u where i am

Which part i know

[sharp storm]

Tell me

[knotty nexus]

So i know i need to make it so that the first top left row to be the number 1

Wait wtf why is there x

I just realized theres x

[sharp storm]

Take the coefficients of the unknowns

[knotty nexus]

So 2x i need to turn into 1?

[sharp storm]

No

https://youtu.be/eYSASx8_nyg?si=fKejwsR3VrwKeFTH

[knotty nexus]

Ohhhh

The thumbnail explain it i think

[sharp storm]

You might wanna watch this video

[knotty nexus]

Because my teacher, or professor, idk who u call them but they dont have x y and z

Okay imma go back to u after the watch

[sharp storm]

Cuz they only takes the coefficients

[knotty nexus]

Ohh okay

Wait wait

U know any video that explain not the jordan?

Because for my hw. The first 2 it needs to be done using normsl gauss

Not the jordan one

Does that exist?

[sharp storm]

Normal gauss ?

[knotty nexus]

Yea

[sharp storm]

I actually call gauss jordan elimination as gauss elimination so its probably just a name

I think its two names for same thing

[knotty nexus]

Not sure, because my prof said its different. But idk

So should i watch the video or should i find another one without the jordan

Will i miss a crucial information

[sharp storm]

https://www.youtube.com/watch?v=eDb6iugi6Uk

Yeah actually i don't make any names difference between both

[knotty nexus]

Theres no difference?

[sharp storm]

Its the same as gauss jordan but you stop when you have 0 ... 01 in the last line on the left

[knotty nexus]

Idk what means

That

So which one i watch first

[sharp storm]

The second one ig

[knotty nexus]

Aight imma come back to u, see if i know anything

Hey

Im confused at minute 3.20

So i know that u need to plus row 1 with row 3

Hey u mind if i ping u

Sorry for being entitled

[fierce flame]

Do you mean with row 2?

[sharp storm]

Yeah you do R3 <- R3 + R1

And R2 <- R2 - 2R1

[knotty nexus]

Row 2 or row3?

[knotty nexus]

What <- mean

[sharp storm]

"become"

[knotty nexus]

So row 2 minus 2 times row 1?

So if row2 is 5 and row 1 is 2 then row 2 become 1?

[sharp storm]

Yea

[sharp storm]

Yep but you do it such that it become 0

[knotty nexus]

How?

[sharp storm]

Its like when you eliminate variable in a 2x2 system of equations

[knotty nexus]

What?

I have no idea what that means

[fierce flame]

By adding to the row by the additive inverse

[knotty nexus]

Whats inverse

[fierce flame]

E.g in your question, to make the element in row 2 column 1 equal 0 you could subtract 3 times row 3

Because 3 + 3*(-1) = 3 - 3 = 0

In this case -3 is the additive inverse of 3

[knotty nexus]

Sorry, let me rewind

So i need to add row 1 and row 3 then that result replace row 3

Then what

[fierce flame]

It’s tricky to keep track of the state when you are just writing out the row operations, have you written down the matrix after each step?

If so send a photo of the current state

[knotty nexus]

2 3 -1 -1
3 -1 7 38
1 2 1 5

Then

2 3 -1 -1
3 -1 7 38
3 5 0 4

Then what

[fierce flame]

Well the objective is to make the first column look like
1
0
0

So what would you do to achieve that

[knotty nexus]

I have no idea

[fierce flame]

Well you could start with the first row

How do you get 1 from 2

[knotty nexus]

Which 1?

Which row

[fierce flame]

First row

You want to make the first column a 1

[fierce flame]

Because this

[knotty nexus]

I thinkcorrect me if im wrong. Divide it by 2

I think idk

[fierce flame]

Yeah, and remember that applies to the entire row

[knotty nexus]

Ohh wait

[fierce flame]

So what is the new state after halving the first row

[knotty nexus]

U cant divide 3 with 2?

Now what

[fierce flame]

3/2 = 1.5

But just leave it as 3/2

[knotty nexus]

Ohh okay i thought its not allowed

-1 divide by 2? -1/2?

[fierce flame]

Yes

[knotty nexus]

1 3/2 -1/2 -1/2
3 -1 7 38
3 5 0 4

[fierce flame]

Normal arithmetic rules apply, you don’t have to keep questioning yourself

[knotty nexus]

Oh wait

U asked before if i should add row 1 with row 2? Is it row 2 or row 3? Because my prof said wirh row 2, but the vid is row 3

[fierce flame]

Ignore what I said before, i thought you were following the example from the video linked

[fierce flame]

Focus on this now

[knotty nexus]

Oh okay

Then what

[fierce flame]

How do you complete the first column to get
1
0
0

[knotty nexus]

I think

Row 2 + row 1 times how much til it become 0?

[fierce flame]

That’s for you to answer

[knotty nexus]

Or 3+(1×-3)?

Im conflicted

[fierce flame]

Yeah this ^

[knotty nexus]

Which one

[fierce flame]

I only see one

3 + (1 x -3)

[knotty nexus]

Oh okay

Im assuming the -3 is the same

With the middle and the right?

-1 + (3/2 x -3)?

[fierce flame]

What ever you do to one part of a row, you must do to the rest of the row

[knotty nexus]

So like this no?

[fierce flame]

Yes

[knotty nexus]

3/2 x -3, how do u calculate it so it doesnt end with 1.5

[fierce flame]

-9/2, you just have to deal with it being a non integer

[knotty nexus]

So the 2 stays?

[fierce flame]

Yes

[knotty nexus]

So -1 + -9/2

Is

-10/2

[fierce flame]

Not quite, -2/2 - 9/2

[knotty nexus]

What??

How

Oh

-1 is -1/1 ?

Then times 2 because to make the bottom the same

No?

[fierce flame]

Yeah -1 = -2/2 = -123/123 = -n/n

[knotty nexus]

Omg im so stupid, because times and add is different

Mybad

[fierce flame]

Where did you get this problem from btw?

[knotty nexus]

Professor. Or teacher. Idk what u call teacher from college

I know britain calls them professor

Or is it the us

[fierce flame]

US

Anyway, complete the second row

[knotty nexus]

1 3/2 -1/2 -1/2
0 -11/2 11/2 73/2
3 5 0 4

This looks wrong

[fierce flame]

7 - 3(-1/2) = 7 + 3/2 = 14/2 + 3/2 = 17/2

[knotty nexus]

Wait why 7-3?

[fierce flame]

38 + 3/2 = 76/2 + 3/2 = 79/2

[knotty nexus]

Im confused

[fierce flame]

Because you are adding -3*(something)

Which is the same as just subtracting 3*(something)

[knotty nexus]

I think i did 7+(-1/2×-3

[fierce flame]

Yeah that is the same as 7 - 3(-1/2)

[knotty nexus]

Ohh

[fierce flame]

So now you have

1 3/2 -1/2 -1/2
0 -11/2 17/2 79/2
3 5 0 4

You repeat the process for the bottom row

[knotty nexus]

Im guessing 3+(0×-3)

Then 5+(-11/2×-3)

0+(17/2×-3)

4+(79/2×-3)

[fierce flame]

You don’t subtract by row 2

[knotty nexus]

Wdym

[fierce flame]

Because if you focus on the first column
1
0
3

You want to get
1
0
0
Using the values from the same column

Which means a row with 0 is useless

So instead you do the same as you did for row 2

Subtract 3 times the first row

So I believe you get

1 3/2 -1/2 -1/2
0 -11/2 11/2 73/2
0 1/2 -3/2 5/2

[knotty nexus]

Wait wait sorry im lost

How do u make 3 turn to 0

[fierce flame]

3 - (3 * 1)

Or rather R3 = R3 - 3*R1

[knotty nexus]

Ohh, but what if row 3 is negative?

[fierce flame]

Then the - becomes +

R3 = R3 + 3*R1

[knotty nexus]

What if the bottom row is not 3? But -5 instead for example. Does it turn to r3=r3+5*r1?

[fierce flame]

If R1 is -1 then yes

[knotty nexus]

Im confused

[fierce flame]

Ultimately you want to use the additive inverse.
Which for any number a, the additive inverse of a is b such that a + b = 0

For example, if a = 5, then b = -5

Do you follow?

[knotty nexus]

So i have to make row 3, turn into 0 no matter what by times the r1 as much as i need

I think

[fierce flame]

Yes

By using other entries in the same column

[knotty nexus]

Okay then what

[fierce flame]

So if I gave you
2
0
-4
What would you do to make the bottom row zero

[knotty nexus]

-4+(2×2)

[fierce flame]

Express it as row operations

[knotty nexus]

R3=R3+2R1

[fierce flame]

Yes! Real simple

One more example

5
3
8
Make the bottom row 0 again

Wait

That instead

[knotty nexus]

Umm since the second row is not 0 so i use 3 instead?

Or i use the top row

[fierce flame]

What do you think you should do

Instinctively

[knotty nexus]

Omg idk. I dont think u can do either of those numbers

[fierce flame]

Take a guess then

[knotty nexus]

But if we made to the last row. The first row should already be 1 tho no?

And second row is 0

[fierce flame]

There is no specific order that you must do, but turning the first row into a 1 first is usually a good direction to head

[fierce flame]

But there are at least three solutions for this

1 is arguably better than the other two

[knotty nexus]

How so

[fierce flame]

Hint: you can use more than one row in an operation

[knotty nexus]

I have no idea, my prof dont explain it that thorough even so i still dont understand his simple explanation

The answer is probably more simple than i thought

Idk

[fierce flame]

You have
5
3
8
And you want to turn 8 into 0 using any or both of the other rows

[knotty nexus]

Ohh u can use 5 and 3?

[fierce flame]

Mhm

[knotty nexus]

8-(5-3)×4

Thats definitely wrong

[fierce flame]

That’s… an interesting choice

It is correct though

But I was looking for 8 - (5+3)

[knotty nexus]

Oh yea i meant to type -

[fierce flame]

So R3 = R3 - R2 - R1

Both ways are valid, but generally try to find the simplest solution

To make things easier for yourself

[knotty nexus]

Oh yea that makes a lot of sense

[fierce flame]

I’m gonna go over two more row operations in case you weren’t sure of them

[knotty nexus]

Wait. I still dont understand gauss jordan and LU

[fierce flame]

Gauss Jordan builds on top of Elementary Row Ops

So it’s best you hear this

1. You can multiply any row by a scalar

You have already been doing this

[knotty nexus]

Whats scalar

[fierce flame]

Scalar can be any real number

[knotty nexus]

Oh okay

[fierce flame]

So an integer, positive or negative

Fractions

[knotty nexus]

Fractions is like 5/5?

[fierce flame]

Even irrational numbers (but avoid this one of course)

Yeah fractions is anything in the form a/b

[knotty nexus]

Aight

[fierce flame]

2. You can swap rows

[knotty nexus]

How that work

[fierce flame]

This one is quite helpful once you get used to Gauss Jordan

And it will speed you up at times

Say you have
2 3 4
5 4 7
1 2 1

If you want row 1 column 1 to be a 1, you can just swap row 1 and 3

So you get
1 2 1
5 4 7
2 3 4

No arithmetic needed

[knotty nexus]

Ohh thats neat

Prof didnt mention that

Or did but i miss it

[fierce flame]

Well keep it in mind

[knotty nexus]

Aight

Thats it?

[fierce flame]

Yeah that’s really all you need to know on Row Ops for now

Back to og question

[knotty nexus]

Okay

[fierce flame]

1 3/2 -1/2 -1/2
0 -11/2 11/2 73/2
0 1/2 -3/2 5/2

Now we work on the second column

You want to get this column to look like
0
1
0

Using any row operations you want, how would you do that

[knotty nexus]

Im thinking but idk

Oh wait

The middle one has to be 1 right?

[fierce flame]

Yes

[knotty nexus]

-11/2 divided by -11/2

Idk

Sorry

[fierce flame]

Yeah, that’s right so far

[knotty nexus]

Really?

I dont need to use the top row?

[fierce flame]

You just need to divide the entire row by -11/2

[knotty nexus]

11/2 : -11/2 is -1?

[fierce flame]

Yes

[knotty nexus]

73/2 : -11/2 im hsving a hsrd time

The result will be negative right

[fierce flame]

Yeah

Remember dividing by a fraction is the same as multiplying by its reciprocal

[knotty nexus]

Whats reciprocal

[fierce flame]

Flipped

So reciprocal of a/b is b/a

[knotty nexus]

What

So 2/73 : -11/2

What

[fierce flame]

You flip the -11/2

So 73/2 / -11/2 = 73/2 * -2/11

[knotty nexus]

Why the -11/2 and not 73/2

That flip

[fierce flame]

Because you want the reciprocal of the fraction you are dividing by

Otherwise the result is flipped

[knotty nexus]

Ohh so the second one that being flipped

Okay

Um i cant turn the 2 to 11

[fierce flame]

What do you mean

Let’s look at this again because we can avoid some fractions here if we use different row ops

1. Add/Subtract
2. Multiply/Divide
3. Swap

[knotty nexus]

Wait wait

73/2 x -2/11. What i need to do is change the 2 to be 11 so i can time it no?

[fierce flame]

When multiplying fractions you just multiply the top and bottom separately

In this case the 2s cancel

[knotty nexus]

So 73x-2 and 2x11?

[fierce flame]

Yes

But the 2s cancel so you get 73/1 x -1/11

[knotty nexus]

Cancel?

Wait u mean 73/-1 x 1/11?

Or the positive and negatives switch?

[fierce flame]

Yeah, because 2/2 = 1/1

[knotty nexus]

Omg my bad

Its my fault

So its 73 times 11 only?

[fierce flame]

$\frac{73}{\cancel{2}} \times \frac{-\cancel{2}}{11}$

[snow parcel]

shsgd

[knotty nexus]

Woah howd u do that

So now its 73x11?

But theres still negative in the -1/11

[fierce flame]

No, now it’s 73 x -1 on top and 1 x 11 on bottom

[knotty nexus]

Ohhh

Do u have to cancel? What if i dont cancel?

[fierce flame]

$\frac{73\times -1}{1\times 11}$

[snow parcel]

shsgd

[knotty nexus]

The result will be different

[fierce flame]

You don’t have to cancel

But if you dont cancel it will be larger numbers

[knotty nexus]

What if i cancel later

[fierce flame]

73x2 = 146
11x2 = 22
So -146/22

You can cancel after yes

So you can divide -146/22 by 2

[knotty nexus]

Im always confused for when to cancel

[fierce flame]

You can cancel when the top and bottom have multiples of each other

[knotty nexus]

Okay so its -73/11

[fierce flame]

Yeah

[knotty nexus]

Oh wow its the same

Okay then what

[fierce flame]

Well you just carry on with the rest of the rows

But

The way we went first time made it harder in the long run

If you were to do it again what would you do first

1. Add/Subtract
2. Multiply/Divide
3. Swap

Those are the row operations available

[knotty nexus]

Swap

I think idk

[fierce flame]

I agree

Which rows

[knotty nexus]

Bottom row

With top row

I think

[fierce flame]

Mhm

Let me format this so it’s readable

[knotty nexus]

Omg i have a headache

Could we take a break

[fierce flame]

Lmao sure

[knotty nexus]

U cs major by any chance?

[fierce flame]

No, i’m guessing you are though?

[knotty nexus]

Yea, idk why they teach me this. I pick cs to avoid math, but turns out its their love interest

[fierce flame]

You probably wanted to do Software Engineering then

CS is a science. All sciences use maths

[knotty nexus]

Damn, too late now

[fierce flame]

Yeah, the maths will come with time and practice though

[knotty nexus]

Yea, especially for me

[fierce flame]

If I were you, I would practice multiplying and adding fractions and maybe algebra too if you’re also weak in that area

Because soon you’ll be taking calculus modules and being held by a weak foundation makes things 10 times harder

[knotty nexus]

Whats algebra

[inland forum]

Wait

Does the question require you to do that

Using matrices

For a systems with 3 variables you can just solve it pretty easily without putting it into matrix form

If you’re not familiar at all with matrices

[gaunt chasm]

Yeah thats how i solved it

[inland forum]

yeah so i recommend for you to be able to try it just as a normal systems if you're struggling unless its required by your course

at the end of the day, learning gauss jordan elimination is relatively unimportant for the sole purpose of solving systems during precalc

you can solve 3x3 systems without using matrices and it adds unnecessary complexity when you'll be introduced to it in more depth in linear algebra is my opinion on it

what a matrix can even represent can be unclear to you when you learn it during this time

some people just know how to solve it initially writing it as an augmented matrix, not even understanding that they're solving the equation Ax=b for the x vector

in my opinion, why even bother
you can solve a system like this just like a normal 2x2 systems
solve for x in terms of y and z with the first equation
then, substitute x in in the 2nd and 3rd equation
then you have the 2nd and 3rd equations both in terms of y and z
treat the 2nd and 3rd equations as a normal system and find the value of z
then use z to find the value of y by plugging into ur 2nd or 3rd equation
and then find the value of x by plugging in y and z into your 1st equation

oh shoot

i didnt notice that the post used to be called "Wth is guass"
i guess the question was asked with GJE in mind

mb