Exercise 2

Diagonalize this matrix by following the steps of Example 2.5.

• 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 two vectors to make a basis. (Consider separately the system in the $x=0$ and $x\neq 0$ cases. Also, recall that the zero vector cannot be a member of a basis.)

• Use that basis in the similarity diagram to get the diagonal matrix as the product of three others.