Hi

can someone explain to be how they get the eigenvectors for the following matrix

hence

eigenvalues are

i get

however answers says when

matrix is

i don't understand how they got this result, someone please explain this to me.

P.S

Printable View

- October 5th 2011, 03:51 AMPaymemoneyBasic probelm on 2x2 Eigenvector
Hi

can someone explain to be how they get the eigenvectors for the following matrix

hence

eigenvalues are

i get

however answers says when

matrix is

i don't understand how they got this result, someone please explain this to me.

P.S - October 5th 2011, 04:07 AMTheChazRe: Basic probelm on 2x2 Eigenvector
(2 - L)^2 - 4 = 0 is the characteristic polynomial.

- October 5th 2011, 09:21 AMHallsofIvyRe: Basic probelm on 2x2 Eigenvector
You are making two errors. The first is in thinking that the row reduced matrix leads to . This really the reduced form of the "augmented matrix"

for solving the matrix equation .

That is, it corresponds to the equation so that you get , not .

Your second error is in thinking you can set v2= 1 to get (using the correct ) and**then**set to get . You can do one or other, not both! If you set v2= 1, you get v1= 1/2 and so have the eigenvector . If you take v1= 1, you get v2= 2 and so have the eigenvector .

Since one is a multiple of the other, both are eigenvectors corresponding to eigenvalue 4. - October 6th 2011, 01:17 AMPaymemoneyRe: Basic probelm on 2x2 Eigenvector
ok i understand now thanks for the explanation