Exercise 3

Follow Example 2.5 to diagonalize this matrix.

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

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

• With that basis use the similarity diagram to get the diagonalization as the product of three matrices.