Question 1
A square matrix is diagonalizable if and only if it has what property?
Question 2
Why is any $3 \times 3$ matrix with three distinct eigenvalues diagonalizable?
Question 3
Which matrix is diagonalizable for the simplest reason that it is already diagonal?
Question 4
A $2 \times 2$ matrix has only one eigenvalue and only one linearly independent eigenvector. Is it diagonalizable?
Question 5
A $3 \times 3$ matrix has eigenspace dimension $2$ for eigenvalue $5$ and eigenspace dimension $1$ for eigenvalue $1$. Is the matrix diagonalizable?
