Re: Equation for eigenline

Hi, I have come across this same example, and I am the same I don't get it. The text says "these equations both reduce to 3x-2y=0. Thus the eigenlines corresponding to the eigenvalue k =4 has the equation y=(3/2)x". I understand that 3x-2y=0 is the same as y=(3/2)x but cannot seem to get my head around how the equations reduce to 3x-2y=0. I'm sure this is just basic manipulation but I can't see it.

Re: Equation for eigenline

Are you referring to the equations x+ 2y= 4x and 3x+ 2y= 4y?

Subtract 4x from both sides of x+ 2y= 4x to get -3x+ 2y= 0. Subtract 4y from both sides of 3x+ 2y= 4y to get 3x- 2y= 0. Those are clearly the same (one is the other multiplied by -1).

Re: Equation for eigenline

Thanks for that, I have tried this on an assignment question, could someone please check? I'm not after the answer, just where I'm going wrong.

A=5 7

-2 -4

I believe the eigen values to be k=3 and -2

This gives me the eigen equations for k=3 5x+7y = 3x and -2x-4y =3y

These I believe cancel down to y=(2/7)x

Which then gives me an eigen vector of 7

2

I have done similar with the second eigen value, I know these are wrong because a subsequent part of the question asks for the pdp-1 which I have carried out and does no bring me back to the original matrix.

I believe the error is with the cancel down which is the bit I cannot grasp...