www . seprodstore . com 77 7 � A 2 2 � system ax by c dx ey f � � � � � � � can be expressed as � AX B , where x y � � � �� � � X can be solved by 1 1 a b c d e f � � � � � � � � ���� � � � � X A B � A 3 3 � system ax by cz d ex fy gz h ix jy kz l � � � � � � � � � � ��� � can be expressed as � AX B , where x y z � � � � � �� � � � � X can be solved by 1 1 a b c d e f g h i j k l � � � � � � � � � � � � ���� � � � � � � � � X A B � Eigenvalues and eigenvectors of A : 1 . det ( ) �� A I : Characteristic polynomial of A 2 . Solution ( s ) of det ( ) 0 � � � A I : Eigenvalue ( s ) of A 3 . v : Eigenvector of A corresponding to the eigenvalue � , which satisfies � � Av v � Diagonalization of A : 1 . 1 2 0 0 0 0 0 0 n � � � � � � � � � � �� � � � � D : Diagonal matrix of the eigenvalues of A 2 . � � 1 2 n � V v v v : A matrix of the eigenvectors of A 3 . 1 1 n n � � � � � A VDV A VD V SUMMARY POINTs