Hi,

I have this problem I'm stuck on:

A is a 3x3 matrix

A=

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 areaandc.

for t=c we get the matrix let it be C. for Cx=0we get the system of linear equations:

(c-a)x_{1}-x_{3}=0

(c-a)x_{2}-bx_{3}=0

likewise, for t=a we get

-1x_{3}=0

-bx_{3}=0

(a-c)x_{3}=0

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!