Exercise 5

If we try to diagonalize the matrix of Example 2.3

using the method of Example 2.5 then what goes wrong?

• Draw the similarity diagram with $N$.

• Set up the matrix-vector equation described in Lemma 2.4 and rewrite it as a linear system.

• By considering solutions for that system, find the trouble. (Consider separately the $x=0$ and $x\neq 0$ cases.)