Hi, for the matrix A =
0 1 0
1 0 0
0 0 2
I have calculated the eigen values, and have successfully calculated the eigen vectors for lamda = -1 and 1. However for lamda = 2 the solutions says the answer is: Eigen vector: A( 0, 0, 1) where A is arbitrary and the vector is a column vector. The problem I am having is seeing where this answer came from.
(A - lamda*I3)*(X, Y, Z) (column vector) = 0
The Attempt at a Solution
As I said above I already know the correct Eigen vector for this particular Eigen value, I just cannot see where the answer has come from. From using the equation above I got the three following equations:
-2X + Y = 0
-2Y = 0
0 = 0
From these equations I cannot see where you get an eigen vector including a value for Z. Any help would be very much appreciated, thanks in advance, Kamran.