Your Practice Set – Applications and Interpretation for IBDP Mathematics
( e ) Hence , express n
M in terms of n .
Let f( n ) be the first diagonal entry of
( f ) Write down lim f( n) . n�� n
M .
[ 3 ]
[ 1 ]
4 . The matrix M is defined by
where �1 � �2.
�3 1�
� M � �
2 2
�. Let � �
1
and �
2 be the eigenvalues of M ,
1 0 � � �
( 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 .
( e ) Hence , express n
M in terms of n .
Let gn ( ) be the last diagonal entry of n
M .
[ 3 ]
[ 3 ]
( f ) Write down lim gn ( ) . n��
[ 1 ]
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