Question

\[x_1' = 6x_1-x_2\\x_2'= -5x_1+2x_2\\x_1''-8x_1'+7x_1=0\]
characteristic equation of it is (r-1)(r-7)=0 which leads to \[x_1= C_1e^t + C_2e^{7t}\]
\[x_2 = D_1e^t +D_2e^{7t}\]
what is the relationship between \(C_1,
C_2~and~~D_1,D_2\)
Please

Answer 1

I can't read it

Answer 2

can you? or let me scan another one?

Answer 3

Okay well those coefficients will be the eigen vectors.

Answer 4

They are components of the eigen vectors.

Answer 5

So they will be proportional to the eigen vectors

Answer 6

proportional? what do you mean?

Answer 7

Do you know what an eigen vector is?

Answer 8

but that comes from differential equation course, not from linear algebra.

Answer 9

oh hi thar

Answer 10

hmm they have 2 unique roots...can't you just put that? O_O

Answer 11

yes we can, @UsukiDoll

Answer 12

I'm studying that now and I haveyet to finish my proofy thingy .x.xx.x

Answer 13

oh I'm using y'' y' in my course

Answer 14

hm they both have the same real roots...

Answer 15

your course doesn't finish yet. wait, at the end of the semester, you will have this stuff, x' = A x , and you have to go backward to set x = Sy , solve for y and back there to solve for x (x, y are vectors)

Answer 16

ya + I have to use Laplace.

Answer 17

is that a linear operator? hmm those are fun

Answer 18

maybe next semester, you will be at my course now: combination between diff and linear algebra. ha!! it kills me

Answer 19

ummm I don't have to take that course

Answer 20

because I took a writing intensive elementary linear algebra course and got credit for it. you can only get credit for that or math 307 which is what you mentioned

Answer 21

ok, me not, I have to. and some more because my major is math

Answer 22

same but it's stressful as BEEP!

Answer 23

engineer students will stop at diff. course. to math students, that course is middle one ( for BS)

Answer 24

can you glance at my proof problem ? ^^

Answer 25

nope. battery is low. I saw yours something like (D-r)^k .... right? I don't understand a word

Answer 26

oh you're on a laptop?

Answer 27

no, I mean my "battery". it's so late here and I am tired. anyway, where is your post. hey. wio, tkunny, primegraph are special ones, why don't you task them?

Answer 28

*tag , not task

Answer 29

alright...but do you know another term for linear operator? I want to get more practice out of it but I can't find sufficient pdf files

Answer 30

hey, I saw zarkon, one of lions in this site. tag him

Answer 31

where is your post?

Answer 32

got it..

Answer 33

one of lions
?

Answer 34

I mean experts. you know, sometimes, especially when you are sad or tired, you don't want to engage to a heavy stuff. That's why sometimes, when we tag, the persons who you know they can help ignore us. ha!! sadly that's true but understandable.

Answer 35

I go to bed now. still have a bunch of homework not done yet. whatever, sleepy

Answer 36

see you tomorrow

Answer 37

alright I have to practice some stuff as well...