Your Practice Set – Applications and Interpretation for IBDP Mathematics
29
Paper 2 – Eigenvalues and Eigenvectors
Example
The matrix A is defined by
where �1 � �2.
��2 1� A � � � . Let �
1
and �
2 be the eigenvalues of A ,
��5 4�
( a ) Find the characteristic polynomial of A .
( b ) Hence , write down the values of �
1
and �
2
.
Let v
1
and v
2 be the eigenvectors of A corresponding to �
1
and �
2 respectively .
[ 2 ]
[ 2 ]
( c ) Write down v
1
and v
2
.
It is given that det ( A ) � ��1�
2, 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 , express n
A in terms of n .
[ 3 ]
[ 3 ]
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