Chapter 8.4, Problem 19E

Let P denote a matrix whose columns are eigenvectors K₁, K₂ … K_n corresponding to distinct eigenvalues λ₁, λ₂,…, λ_n of an n × n matrix A. Then it can be shown that A = PDP^–1, where D is a diagonal matrix defined by

     $D=\left(\begin{array}{cccc}{\lambda }_1& 0& \cdots & 0\\ 0& {\lambda }_2& \cdots & 0\\ ⋮& ⋮& & ⋮\\ 0& 0& \cdots & {\lambda }_n\end{array}\right)$    (9)

In Problems 19 and 20 verify the foregoing result for the given matrix.

19. $A=\left(\begin{array}{cc}2& 1\\ -3& 6\end{array}\right)$