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## Homework Statement

Define T in L(F

^{3}) by T(z1, z2, z3) = (2*z2, 0, 5*z3). Find all eigenvalues and eigenvectors of T.

## Homework Equations

## 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.

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