matrix

[weak lily]

matrix

how can we solve this equation for x

[fair pagoda]

First, simplify the matrix on the RHS by factoring 5 inside of it.
Then, subtract that matrix from both parts.
Finally, multiply both parts by -(1/2). That will allow you to express X.

[weak lily]

can you solve the whole question for me

its a very important homework for me

and i couldn't solve due to my unawareness

🙏

[fair pagoda]

Um, no. Try it yourself first.

[weak lily]

i dont know what does RHS mean... i tried but i couldn't solve it.

can you please help me about finding the answer

its really important...

[lunar quail]

right hand side

[weak lily]

what does it mean

right hand side

[lunar quail]

it means the right hand side

[weak lily]

im not into matrix

so i couldnt understand

sorry

would you please help me sir

[lunar quail]

reading comprehension has nothing to do with math

"the matrix on the right hand side"

if you know what a matrix is

and know what "right" and "side" mean from your elementary days, you can put two and two together to understand what it means

but anyway, how would you solve something like 7=-2x+3?

[weak lily]

what

x=-2

[lunar quail]

how?

show your work

[lunar quail]

do the same thing here then

just with matrices instead of numbers

[weak lily]

can you teach me

[lunar quail]

no

[weak lily]

sure

[fair pagoda]

It's literally the same as with a simple linear equation, though.

[lunar quail]

looking at it entrywise, you're just solving 6 equations akin to 7=-2x+3

[weak lily]

you are just bullying me with your knowledge man, there is no shame in not knowing the shame lies in not finding out

and i just wanted to learn sth

[lunar quail]

then attend class

[weak lily]

thank you anyway

[fair pagoda]

Sorry, but you don't seem to even be trying to do anything. You just want us to solve it for you.

[lunar quail]

You've demonstrated you know the process, you just need to sit there and do it

[weak lily]

i didnt want the answer directly

just tell me steps

and how to do them

[lunar quail]

we did

[fair pagoda]

I already did.

[lunar quail]

you're doing the exact same thing

but with matrices, instead of numbers

the exact same idea of addition and scaling hold, and are done in the "no shit sherlock" manner

[weak lily]

First, simplify the matrix on the RHS by factoring 5 inside of it.

how can i do this step

tell me

[lunar quail]

$c[A_{ij}]=[cA_{ij}]$ entrywise

[dense lark]

omegabet_

[weak lily]

lets be solution oriented

[lunar quail]

for any scalar $c$ and matrix $A:=[A_{ij}]$

[dense lark]

omegabet_

[weak lily]

whats that man

what are you doing rn

[lunar quail]

that's how you multiply a matrix by a scalar

you just multiply each entry of A.. by the scalar

[fair pagoda]

Why are so many people so incredibly strongly opposed to solving things generally? I can't understand it...

[lunar quail]

Likewise, as you will recall from your notes/lecture/class whatever, $[A_{ij}]+[B_{ij}]=[A_{ij}+B_{ij}]$, provided $A$ and $B$ are of the same size

[dense lark]

omegabet_

[fair pagoda]

The individual task is not what's important. The general principles and algorithms is what's important.

[weak lily]

guys i tried to solve this equation

11/10 -15/2 -23/4
-41/10 7/2 45/4

is that correct answer

what do you think

i done all of the steps

@lunar quail @fair pagoda

[lunar quail]

post your steps

[fair pagoda]

No. Can you show what you've done?

[weak lily]

matrix x = a,b,c,d,e,f

1 = (-2a + 5)(-5) + (-2b + 5)(-3) + (-2c + 5)(-4)
7 = (-2a + 5)(-5) + (-2b + 5)(-1) + (-2c + 5)(-4)
-6 = (-2d + 5)(-5) + (-2e + 5)(-3) + (-2f + 5)(-4)
9 = (-2d + 5)(-5) + (-2e + 5)(-1) + (-2f + 5)(-4)

then i simplified this

into this

1 = 10a - 25 + 6b - 15 + 8c - 20
7 = 10a - 25 + 2b - 5 + 8c - 20
-6 = 10d - 25 + 6e - 15 + 8f - 20
9 = 10d - 25 + 2e - 5 + 8f - 20

more simplifiements

10a + 6b + 8c = 61
10a + 2b + 8c = 57
10d + 6e + 8f = -16
10d + 2e + 8f = -26

[lunar quail]

that looks like complete nonsense

[weak lily]

why

[lunar quail]

cause it's wrong

[weak lily]

its my own method

[lunar quail]

by your notation, you have $1=-2a+5(-5), 7=-2b+5(-5)$, etc

[dense lark]

omegabet_

[lunar quail]

since, again, + and scaling is done component wise

[weak lily]

guys i need to find c1 and c2

can you help me

btw the other question is solved by me

i found my mistake

and i fixed it

[fair pagoda]

Note that by Cayley-Hamilton a matrix must satisfy its own characteristic polynomial. So, find it.
To remind you, you can find it as det(M - λI), which will be a polynomial in λ.

[weak lily]

i just found the determinant of this 2x2 matrix

its -36

[lunar quail]

I feel like if they're just learning matrix algebra, they wont know Cayley Hamilton

[weak lily]

i know the hamiltons theorem bro

[lunar quail]

I somehow doubt that but ok

[weak lily]

but i couldn't solve this question

what should i do

i dont know

[lunar quail]

then just apply CH as was said

[weak lily]

i heard about the theorem but im not into it

[lunar quail]

then you dont know "the hamiltons theorem"

[weak lily]

i know

[lunar quail]

then apply it..

[weak lily]

i just dont have detailed information about it

[lunar quail]

what does CH say then?

[weak lily]

do you know the human anatomy omegabet

[lunar quail]

that's relevant how?

[weak lily]

for example do you know our lungs?

yes or no

simple

[lunar quail]

what does the Cayley Hamilton theorem say?

[weak lily]

please answer my question

do you know human lungs

[lunar quail]

Please answer my question

Cause you're the one here asking for help

[fair pagoda]

Uh, Bugra, if you say you know a theorem, be prepared to formulate it. Otherwise it just seems that you are lying.

[weak lily]

okay

let me tell you

but promise me

then you will answer my question omegabey

t*

[lunar quail]

When you tell me how my knowledge of lungs is at all relevant to matrix algebra, and after you have answered my question, then sure I'll humor you

[weak lily]

hamilton says that a characteristic polynomial expression of a real square matrix should be equal to zero matrix

[lunar quail]

so apply it

[weak lily]

also it can be complex square matrix

then

do you know our lungs

yes you know our lungs

[lunar quail]

yes, I know what lungs are

[weak lily]

okay

how does it work

can you explain me

no

you cant

so you dont know lungs

that what you said

thats

[lunar quail]

So you know the theorem, but you don't what the theorem says?

That right there is a bit of a paradox, math theorems arent like lungs

[weak lily]

i told you what the theorem says

[lunar quail]

so apply it then

the theorem tells you what it does

[weak lily]

there are god but we cant see him

so there are no god?

[fair pagoda]

It seems that you just want to fool around instead of discussing your question. I won't bother anymore with this.

[lunar quail]

There are atoms but we can't see them, so there are no atoms?

[weak lily]

I do not intend to joke

[lunar quail]

Well anyway you have the answer to your question, gl

[weak lily]

omegabet is just bullying me

and you are just ignoring it

lorddarpinger

[lunar quail]

and you're wasting my time and your own

[weak lily]

he is putting pressure on me about hamilton

ofc i know what he says

[lunar quail]

You've answered your question yourself, just apply CH. gl

[weak lily]

lol

its just funny that you equate theoretical and practical studies

cya