## Mimi_x3 one year ago i have problems with finding eigen vectors

1. Mimi_x3
2. Mimi_x3

i get stuck here|dw:1439628997200:dw|

3. Mimi_x3

is there like a legitmate resource in finding eigen vectors

4. Empty

Crap it cut off your vector there on the equal sign

5. Mimi_x3

i feel as though i'm just guessing

6. Empty

I'm a legitimate resource bb

7. Mimi_x3

crap what

8. Mimi_x3

bb you're never there for me

9. Empty

|dw:1439629120440:dw|

10. Mimi_x3

IM UNDATEABLE APPARRENTLY

11. Mimi_x3

oh |dw:1439629144430:dw|

12. Empty

13. Mimi_x3

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

14. Mimi_x3

|dw:1439629180128:dw|

15. Empty

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

16. Mimi_x3

-3iv1 = -3v2 v_1 = - iv_2

17. Mimi_x3

v_2 = iv_1

18. Empty

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

19. Mimi_x3

WAIT

20. Mimi_x3

isnt v_2 = iv_1

21. 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|

22. Mimi_x3

omg you're a god

23. Empty

;) yw bb

24. Mimi_x3

can you be here for me

25. Empty

i AM here 4 u

26. Mimi_x3
27. Mimi_x3

I don't get the formula for one real value

28. Mimi_x3
29. Mimi_x3

what is that 1 I thing doing

30. Empty

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

31. Mimi_x3

|dw:1439629654953:dw|

32. Mimi_x3

the eigen vector

33. Mimi_x3

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

34. Empty

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

35. Mimi_x3

isn't that suppose to be 0 0

36. Mimi_x3

I'm asking how to plug into formula

37. Mimi_x3
38. 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.

39. Mimi_x3

I have solution

40. Mimi_x3

which i don't get

41. Empty

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

42. Mimi_x3

no idea

43. Mimi_x3

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

44. 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

45. Mimi_x3

|dw:1439629912004:dw|

46. Mimi_x3

ok i get above^ just plugging in

47. Mimi_x3

|dw:1439629999156:dw|

48. Mimi_x3

I HAVE NO CLUE FOR THIS PART^

49. Empty

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

50. Mimi_x3

ok

51. Empty

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

52. Mimi_x3

yeah

53. Mimi_x3

but i don't get how u got to it

54. Empty

ok circle the steps that don't make sense

55. Mimi_x3

|dw:1439630519158:dw|

56. Mimi_x3

from here |dw:1439630544936:dw|

57. 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. ;)

58. Empty

I gotta go to sleep soon

59. Empty

gn bb xoxo

60. Mimi_x3

:( you left me

61. Mimi_x3

BUT THANK YOUUU LOVE U FOR LIFE

62. Mimi_x3

if you do come back

63. Mimi_x3

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

64. 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 $x_1= y_1 \\ y_2= x_1+x_2 \rightarrow x_2= y_2 -y_1$