anonymous
  • anonymous
Determine if (3+i -2) is an eigenvector of the matrix (-1 -2 / 5 -7) .. not division but under the first to numbers
Mathematics
katieb
  • katieb
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anonymous
  • anonymous
use the definition
anonymous
  • anonymous
if you multiply them do you end up with a scalar multiple of the matrix you started with? ( I am fairly sure thats the definition from memory )
anonymous
  • anonymous
snce there are complex numbers I dont think its possible

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anonymous
  • anonymous
Av = Yv
anonymous
  • anonymous
oh and that -2 is under the i
anonymous
  • anonymous
y is lamda?
anonymous
  • anonymous
yeh
anonymous
  • anonymous
lol
anonymous
  • anonymous
so the vector with two components is ( ( 3+i) , -2 ) ?
anonymous
  • anonymous
Well it's written as a matrix
anonymous
  • anonymous
fairly sure answer is no
anonymous
  • anonymous
Yes that is right. Did you just use the formula? How did you know it wasn't the vector?
anonymous
  • anonymous
if you multiply them together you get ( -(7+i) , (1+5i) ) This is not a scalar multiple of the vector you started with
anonymous
  • anonymous
Okay, so it can be a multiple?
anonymous
  • anonymous
no
anonymous
  • anonymous
\[Av=\lambda v\] thats the definiton
anonymous
  • anonymous
we multplied the two component vector with the matrix , and we didnt get a scalar multiple of the original vector , it doesnt satisfy the definition
anonymous
  • anonymous
Oh okay, thank you!

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