I have this problem I'm stuck on:
A is a 3x3 matrix
a,b,c are real numbers
1) determine for what values of a,b,c the matrix A is diagnoizable. (advice: distinguish between the cases a=c and a=\=c)
My attempt at a solution has been finding det(tI-A)=0 , the characteristic polynomial is (t-c)(t-a)^2 and therefore the eigenvalues are a and c.
for t=c we get the matrix let it be C. for Cx=0 we get the system of linear equations:
likewise, for t=a we get
Now, when I tried to find the eigenspaces that correspond to a and c to find out their dimensions I got pretty lost.
I have no idea what to do. help would be very welcomed!