Question

Question 3 (20 Points): Show that the given matrix A satisfies(A − rI)k = 0 for some number r and some positive integer k and use this fact to determine the matrix eªt and solve the homogeneous system x' = Ax where A is given by \mathbf{A}=\left[\begin{array}{cc}

3 & -2 \\

0 & 3

\end{array}\right]

Fig: 1

Fig: 2