and

I could find the eigenvector when

but how do i find the eigenvector when ?

I came up with

but the answer is and

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- January 7th 2012, 03:17 PMBabyMiloEigenvector problem

and

I could find the eigenvector when

but how do i find the eigenvector when ?

I came up with

but the answer is and - January 7th 2012, 05:58 PMHallsofIvyRe: Eigenvector problem
As you say in your first line, the eigenvalues are 1 and -8 so there is no eigenvector for . Was that a typo?

By definition, if is an eigenvector corresponding to eigenvalue -8, then we must have

That is equivalent to the two equations -5x+ 3y= -8x and 6x- 2y= -8y which then give 3y= -3x and 6x= -6y both of which are equivalent to y= -x. Any vector of the form , which, of course, includes , is an eigenvector corresponding to eigenvalue -8. - January 8th 2012, 05:59 AMBabyMiloRe: Eigenvector problem