i have problems with finding eigen vectors

- Mimi_x3

i have problems with finding eigen vectors

- Stacey Warren - Expert brainly.com

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- schrodinger

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- Mimi_x3

https://gyazo.com/355c33166a1edf8139c5331e6e525dc0

- Mimi_x3

i get stuck here|dw:1439628997200:dw|

- Mimi_x3

is there like a legitmate resource in finding eigen vectors

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## More answers

- Empty

Crap it cut off your vector there on the equal sign

- Mimi_x3

i feel as though i'm just guessing

- Empty

I'm a legitimate resource bb

- Mimi_x3

crap what

- Mimi_x3

bb you're never there for me

- Empty

|dw:1439629120440:dw|

- Mimi_x3

IM UNDATEABLE APPARRENTLY

- Mimi_x3

oh |dw:1439629144430:dw|

- Empty

Shhhh I'm trying to help you eigenvectorsize

- Mimi_x3

pls do... I have no idea with this course

- Mimi_x3

|dw:1439629180128:dw|

- Empty

Ok so first off, just multiply the vector with the first row of this matrix. What do you get?

- Mimi_x3

-3iv1 = -3v2
v_1 = - iv_2

- Mimi_x3

v_2 = iv_1

- Empty

Perfect, so now we can plug this in to your vector (v_1, v_2) to get this: |dw:1439629321422:dw|

- Mimi_x3

WAIT

- Mimi_x3

isnt v_2 = iv_1

- Empty

So your eigenvector is (-i, 1), and the v_2 is just an arbitrary constant showing you you can multiply your eigenvector by any constant. So now multiply your vector by i and see it desn't matter: |dw:1439629416364:dw|

- Mimi_x3

omg you're a god

- Empty

;) yw bb

- Mimi_x3

can you be here for me

- Empty

i AM here 4 u

- Mimi_x3

https://gyazo.com/57ff65da1ee195dad40b72621f15dca7

- Mimi_x3

I don't get the formula for one real value

- Mimi_x3

https://gyazo.com/cbb81b2511c7aa5f2042c6ddd3d3389f

- Mimi_x3

what is that 1 I thing doing

- Empty

Oh I don't know I need to solve it give me a sec unless you have something solved

- Mimi_x3

|dw:1439629654953:dw|

- Mimi_x3

the eigen vector

- Mimi_x3

so now plugging into the formula which i don't get

- Empty

so wait real fast you're asking: |dw:1439629691610:dw|

- Mimi_x3

isn't that suppose to be 0 0

- Mimi_x3

I'm asking how to plug into formula

- Mimi_x3

https://gyazo.com/e5a65ed4111fcbcb257ed0465a3efaba

- Empty

I don't know, I need to review it's been a while since I've done these so I kinda forget like minor stuff.

- Mimi_x3

I have solution

- Mimi_x3

which i don't get

- Empty

what's that fancy 1, like I think it's a vector with two 1s in it? |dw:1439629848428:dw|

- Mimi_x3

no idea

- Mimi_x3

I HAVE NOT TAKEN MATHS FOR 2 years :((((

- Empty

It's ok I'll help figure it out. I know that repeated eigenvalues are weird though, so you might just have to memorize this trick, I think you just multiply by t honestly they're making it look more complicated than it should be I think cause they're retarded

- Mimi_x3

|dw:1439629912004:dw|

- Mimi_x3

ok i get above^ just plugging in

- Mimi_x3

|dw:1439629999156:dw|

- Mimi_x3

I HAVE NO CLUE FOR THIS PART^

- Empty

Ok I think I got it give me a sec I don't wanna tell you wrong stuff

- Mimi_x3

ok

- Empty

Ok ok, so now we can multiply to get: |dw:1439630308680:dw| I think that should work

- Mimi_x3

yeah

- Mimi_x3

but i don't get how u got to it

- Empty

ok circle the steps that don't make sense

- Mimi_x3

|dw:1439630519158:dw|

- Mimi_x3

from here
|dw:1439630544936:dw|

- Empty

oh ok I forgot to include that! I realized that fancy 1 was the identity matrix: |dw:1439630629121:dw| then plugging in from there we have: |dw:1439630686461:dw| so that's what leads to this step here: |dw:1439630539112:dw|
I kinda skipped some steps but circle anything else that bothers you so I can explain it more. ;)

- Empty

I gotta go to sleep soon

- Empty

gn bb xoxo

- Mimi_x3

:( you left me

- Mimi_x3

BUT THANK YOUUU LOVE U FOR LIFE

- Mimi_x3

if you do come back

- Mimi_x3

https://gyazo.com/2106cd0c4185f371f26e9a1ed67e7d0c
i don't get this one

- phi

It is not clear how to proceed other than "pattern match"
\[ \dot{x}_1 =x_1+x_2\\ \dot{y}_1= y_2 \]
and try \(y_2= x_1+x_2\)
from which we get \( \dot{y}_2= \dot{x}_1+ \dot{x}_2\)
also, the second equation is
\[ \dot{x}_2 =-2x_1-x_2\]
adding this to the first
\[ \dot{x}_1 =x_1+x_2 \]
we get
\[ \dot{x}_1 +\dot{x}_2=x_1+x_2-2x_1-x_2 =-x_1 \]
or, using our "guess"
\[ \dot{y}_2= - x_1 \]
which is consistent with \(y_1= x_1\)
in other words, make the substitutions
\[ x_1= y_1 \\ y_2= x_1+x_2 \rightarrow x_2= y_2 -y_1\]

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