Question

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

Answer 1

use the definition

Answer 2

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 )

Answer 3

snce there are complex numbers I dont think its possible

Answer 4

Av = Yv

Answer 5

oh and that -2 is under the i

Answer 6

y is lamda?

Answer 7

yeh

Answer 8

lol

Answer 9

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

Answer 10

Well it's written as a matrix

Answer 11

fairly sure answer is no

Answer 12

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

Answer 13

if you multiply them together you get ( -(7+i) , (1+5i) )

This is not a scalar multiple of the vector you started with

Answer 14

Okay, so it can be a multiple?

Answer 15

no

Answer 16

\[Av=\lambda v\]

thats the definiton

Answer 17

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

Answer 18

Oh okay, thank you!