Find the general solutions of Y`=AY

[uncut birch]

A=(4 -2 2
-5 7 -5
-6 6 -4)

i want to know if i did the computation right, especially for finding out the eigenvalues and solving the system when lamda=3, because it looks a bit sus

[fleet yarrow]

are you trying to find the eigenvalues/vectors of Ay=by

where b is a constant

[uncut birch]

yeah

i am finding the eigenvalues and eigenvectors of A to solve the system Y`=AY

[fleet yarrow]

usually we write it in my linear algebra class as Ax=(lambda)x

where lambda is a scalar

[uncut birch]

yeah i see the connection, but i think it's different

Y`=AY and i'm looking for solutions of the form Y(t)=(e^lamda*t)v

where lamda are the eigenvalues of the matrix A and v is the corresponding eigenvector

[fleet yarrow]

so you're basically trying to find values of lambda and the corresponding vectors x right?

[uncut birch]

yes

[fleet yarrow]

do you use matlab?

[uncut birch]

a bit

i had a course last year.. i forgot most of it

[fleet yarrow]

are you allowe matlab on exams?

[uncut birch]

nope, only writing

[fleet yarrow]

there is a command in matlab to give you the coefficients of that polynomial

[fleet yarrow]

note that matlab always make the leading coefficient 1

[uncut birch]

bruh

oh wait

i forgot

i'm working on another exercise now sorry

[fleet yarrow]

i got different

[uncut birch]

yeah it's different matrix

[uncut birch]

so this is correct to the original post

now im working on a new matrix which i cant find the eigenvalue at all xD

and apprently in the program it's with complex number

so that means that the original exercise is wrong?

[fleet yarrow]

the eigen values of the problem you posted oriignally was 3 and 2 which you got

[uncut birch]

yes

[fleet yarrow]

so what is this new problem?

complex eigenvalues just means that the polynomial has complex roots

[uncut birch]

A=(2 -1 2
5 -3 3
-1 0 -2)

so i got like this

using this code

[fleet yarrow]

its jsut 1 and -1

[fleet yarrow]

oops, you put in a 2 when it should be a -2

[uncut birch]

ah lol

[fleet yarrow]

that last entry should be -2

[uncut birch]

yeah i got it now

thank you

anyways, at the first problem

at this system exactly, where i tried to find the geometric multiplicity of lamda=3

did i do it right?

[fleet yarrow]

aren't you suppose to use matrix

[uncut birch]

well yeah

the system is from the matrix

from this one

[fleet yarrow]

so solve it using either matrix inversion or rref

[uncut birch]

isn't it only -1?

[fleet yarrow]

oh yea i don't know why i saw a 1 there

[uncut birch]

hmm

i got -1/3, 5/6, 1

weird

maybe the program doesnt take into account that c is arbitrary

[fleet yarrow]

that scorrect

[uncut birch]

so when we do c(vector) it's 1 in that spot

and the sign shouldnt matter right

[fleet yarrow]

because that's saying that a + 1/3c = 0 so when c is 1 a=-1/3

and b-5/6c = 0 so when c is 1 b = 5/6

so (-1/3, 5/6, 1) is a solution

[uncut birch]

yeah

perfect

cool that i can correct with matlab

thats a good idea

ill try to use from now on

can u send me the program?

[fleet yarrow]

matlab costs money

try scilab

[uncut birch]

i have from uni

4 year

free

matlab, autodesk

[fleet yarrow]

your universe paid for matlab?

[uncut birch]

yes

i study mechanical engineering at my capitals top university

😭

[fleet yarrow]

just search up matlab and log into your account

[uncut birch]

idk how im so stupid

yeah i mean im logged in right now

i just havent used it in a very long time

[fleet yarrow]

you're ysing the script?

[uncut birch]

is it any good?

i tried using it

[fleet yarrow]

i just use the command window for temporary stuff

[uncut birch]

oh

[fleet yarrow]

i use the scripts for projects

[uncut birch]

oh wait

im not sure what the difference it

we only worked with scripts

how can i use the command window

[fleet yarrow]

just type it as if it was a script

and you will get the code output in the same window as where you type the code