Define T in L(F3) by T(z1, z2, z3) = (2*z2, 0, 5*z3). Find all eigenvalues and eigenvectors of T.
The Attempt at a Solution
Well, since we want to find all the eigenvalues, we want the following equation to hold:
T(z1, z2, z3) = (2*z2, 0, 5*z3) = [tex]\lambda[/tex](z1, z2, z3).
Setting up a system of equations, I get the following:
[tex]\lambda[/tex]z1 = 2*z2
[tex]\lambda[/tex]z2 = 0
[tex]\lambda[/tex]z3 = 5*z3
Solving, I get one eigenvalue, namely 5. Then I came up with the corresponding eigenvector, (0, 0, 5). Is this correct?
Edit: 0 is the other eigenvalue, but I don't know what the corresponding eigenvector would be.