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## anonymous 5 years ago Determine if (3+i -2) is an eigenvector of the matrix (-1 -2 / 5 -7) .. not division but under the first to numbers

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1. anonymous

use the definition

2. 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 )

3. anonymous

snce there are complex numbers I dont think its possible

4. anonymous

Av = Yv

5. anonymous

oh and that -2 is under the i

6. anonymous

y is lamda?

7. anonymous

yeh

8. anonymous

lol

9. anonymous

so the vector with two components is ( ( 3+i) , -2 ) ?

10. anonymous

Well it's written as a matrix

11. anonymous

fairly sure answer is no

12. anonymous

Yes that is right. Did you just use the formula? How did you know it wasn't the vector?

13. anonymous

if you multiply them together you get ( -(7+i) , (1+5i) ) This is not a scalar multiple of the vector you started with

14. anonymous

Okay, so it can be a multiple?

15. anonymous

no

16. anonymous

$Av=\lambda v$ thats the definiton

17. 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

18. anonymous

Oh okay, thank you!

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