Exercise 1.6.19

If the eigenvalues of $A$ are 2, 2, 5 then

• 1.

  $A$ is invertible: True since no zero eigenvalues, so nullspace has dimension zero. (wrong answer: False, only if $A$ has full rank.)

• 1.

  $A$ is diagonalizable: False, if $\mathit{GM}<\mathit{AM}$ it’s not diagonalizable.

• 1.

  $A$ is not diagonalizable: False, if $\mathit{GM}=\mathit{AM}$, it diagonalizable.