Diagonalizable matrices help - find matrix P and D

[MaryStew]

For the matrix below, provide a P and a diagonal matrix D such that A=PDP^−1

So I know that I'm supposed to subtract the eigen values λ=1−2i,1+2i diagonally from the matrix below and then use RREF until each matrix is simplified. I'm confused as to what I would do because there are only 2 eigen values but there are 4 columns. Would the other two columns just be filled with 0?

I pressed enter with my answers below but it says my answer is wrong. I'm stumped as to what I'm doing wrong, can someone explain?

 

[Steven G]

What are the steps to get P and D? Can you post your work so we can see what is going on?

 

[HallsofIvy]

For one thing, you are told that the eigenvalues are "1- 2i" and "1+ 2i" but your diagonal matrix has two "0"s on the diagonal. Are you assuming that "0" is also an eigenvalue when you were told it was not?

I would interpret that as meaning that "1- 2i" and "1+ 2i" are the only eigenvalues. (Do you see the difference between "the eigenvalues are 1- 2i and 1+2i" and "1- 2i and 1+ 2i are eigenvalues"?)

If the matrix is diagonalizable you know that there must be 4 independent eigen vectors- either two for each eigen value or one for one eigenvalue and three for the other. What are those eigenvectors?