EXERCISES

1. (10) Let
   
   $$A = \left( \begin{array}{ccc} -1 & 2 & 3 \\ 0 & 2 & 1 \\ 1 & -2 & 2 \end{array}\right)$$
   
   
   1. Calculate the determinant of $A$.
   2. Calculate the trace of $A$.
   3. Calculate the rank of $A$.
   4. What is the rank of $A^T$.

2. (10) Let
   
   $$B = \left( \begin{array}{cc} 5 & -3 \\ -3 & 2 \end{array}\right)$$
   
   
   Calculate the eigenvalues and eigenvectors of $B$.