Let \(A=\left(\begin{array}{lll}1 & 1 & 2 \\ 1 & 1 & 2 \\ 1 & 1 & 2\end{array}\right)\).

a) What is the dimension of the image of \(A ?\) Why?

b) What is the dimension of the kernel of \(A ?\) Why?

c) What are the eigenvalues of \(A ?\) Why?

d) What are the eigenvalues of \(B:=\left(\begin{array}{lll}4 & 1 & 2 \\ 1 & 4 & 2 \\ 1 & 1 & 5\end{array}\right) ?\) Why? [HiNT: \(\left.B=A+3 I\right]\).