i am supposed to determine the eigenvalues and eigenvectors of:
I calculated the eigenvalues with the formula:
to be and
To get the eigenvectors i need to solve the following equation, right?
Now i get x = 0 and y = 0, but thats just not right says Wolfram Alpha and the exercise text.
What is wrong?
if λ is an eigenvalue for A, then Av = λv, for some eigenvector v. which means that
(A - λI)v = 0. this is the system you have to solve (for each value of λ). so for λ1 = (1/2)(1 + √5) this would be:
[(1/2)(1 - √5) ...........1........][x]....
[.......1.......... (-1/2)(1 + √5)][y] = , which leads to:
y = (-1/2)(1 - √5)x.
if we choose (as apparently wolfram|alpha) did, y = 1, this makes x = (1/2)(1 + √5).
you should be able to compute the 2nd eigenvector, now.