Eigenvalues for matrices proof

1. Apr 8, 2010

gutnedawg

Let C be a 2 × 2 matrix such that x is an eigenvalue of C with multiplicity two
and dimNul(C − xI) = 1.
Prove that C = P |x 1|P^−1
|0 x|
for some invertible 2 × 2
matrix P.

I'm not sure where to start

EDIT
|x 1|
|0 x| is the matrix I don't know why it's not posting the way I want it

2. Apr 9, 2010

Eynstone

Consider P which makes C upper diagonal & use the nullity condition.