Define the linear transformation TA(v) = A(v) where (v) is the co-ordinate vector

Question

I'm having some problems with this question. Could someone point me in the right direction? Thanks

Answer 1

Hints:

1) $\,\det(\lambda I-A)=(\lambda +2)^2=0\Longleftrightarrow \lambda =-2\,$

2) Solve the homogeneous system

$$(-2I-A)\binom{x}{y}=\binom{0}{0}$$

Its solution gives you the eigenvectors of $\,A\,$

3) Solve the rest of the exercise...