Your Practice Set – Applications and Interpretation for IBDP Mathematics
SUMMARY POINTs
� Terminologies of matrices : �a11
0 0 � �
� �
0 a22
0
�: Diagonal matrix �
� �
�
� 0 0 ann
� A � det ( A ) : Determinant of A
A is non-singular if det ( A ) � 0
�1
A : Inverse of A
�1
A exists if A is non-singular
� For any 2� 2 square matrices
�a b�
A � � � : �c d�
1 . A � det ( A ) � ad �bc
: Determinant of A
2 .
�1 1 � d �b�
A � � �: Inverse of A ad �bc
��c a �
� Operations of matrices :
1 .
2 .
� a11 a1 n � � b11 b1 n � � a11 �b11 a1 n
�b1
n � � � � � � � � � � a a � �b b � � a �b a �b �
� m1 mn � � m1 mn � � m1 m1 mn mn �
� a11 a1 n � � ka11 ka1
n � � � � � k � � a a � � ka ka � � m1 mn � � m1
mn �
3 . cij � ai 1b1 j
� ai 2b2 j
� � ainbnj
: The element on the i th row and the j th column of
� a11 a1 n ��b11 b1
k � � �� �
C �AB � ��
, where A , B and C
� a a ��b b � � m1 mn �� n1
nk � are m� n, n� k and m� k matrices respectively
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