Let v
1
and v
2 be the eigenvectors of A corresponding to �
1
and �
2 respectively .
( c ) Write down v
1
and v
2
.
It is given that 3det ( A ) ���1�
2�0 , where � � .
[ 2 ]
( d ) Find � .
It is given that matrix . n n �1
A � PD P , where P is a 2� 2 matrix and D is a 2� 2 diagonal
[ 2 ]
( e ) Write down
( i ) P ;
( ii ) n
D .
( f ) Hence , find
10
A , giving the entries in exact values .
[ 3 ]
[ 3 ]
7
3 . The matrix M is defined by
where �1 � �2.
� 1 � �1
M � � 16
�. Let � �
1
and �
2 be the eigenvalues of M ,
�35 2 � � �
( a ) Find the characteristic polynomial of M .
( b ) Hence , write down the values of �
1
and �
2
.
Let v
1
and v
2 be the eigenvectors of M corresponding to �
1
and �
2 respectively .
[ 2 ]
[ 2 ]
( c ) Write down v
1
and v
2
.
It is given that matrix . n n �1
M � PD P , where P is a 2� 2 matrix and D is a 2� 2 diagonal
[ 2 ]
( d ) Write down
( i ) P ;
( ii ) n
D . [ 3 ] www . seprodstore . com
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