Page 6 - M A T R I K S

1  2  2 1   1 + 2 2 +1  3  3
Maka A + B =   +   =   =  
 3 4   − 2 −1   3 + ( − ) 2 4 + ( − ) 1   1 3 

2  0 3  1 5 −  2
Contoh 2: Jika A =   , B =   dan C =   , tentukan :
 1 3   2 4   4 0 
a). A + B b). B + A c). B + C d). A + (B + C) e) A+B f). (A + B) + C

2  0 3  1 5  1
Jawab : a. A + B =   +   =  
 1 3   2 4   3 7 
3  1 2  0 5  1
b. B + A =   +   =  
 2 4   1 3   3 7 
3  1 5 −  2 8 −  1
=
c. B + C =   +    
 2 4   4 0   6 4 

2  0 8 −  1 10 −1 
d. A + (B + C) =   +   = =  
 1 3   6 4   7 7 
2  0 3  1 5  1
=
e. (A + B) =   +    
 1 3   2 4   3 7 
5  1 5 −  2 10 −1 
=
f. (A + B)+C =   +    
 3 7   4 0   7 7 

1  2 −1 −  2 0  0
Contoh 3: Diketahui A =     dan O =   .
+
 3 4   − 3 − 4   0 0 
Tunjukkan : a. A + (-A) = (-A) + A = O
b. A + O = O + A = A

1  2 −1 −  2 0  0
Jawab : a. A + (-A) =   +    
=
 3 4   − 3 − 4   0 0 

−1 −  2 1  2 0  0
=
+
(-A) + A =      
 − 3 − 4   3 4   0 0 

1  2 0  0 1  2
b. A + O =   +    
=
 3 4   0 0   3 4 

0  0 1  2 1  2
=
O + A =   +    
 0 0   3 4   3 4 

Sifat-sifat penjumlahan matriks :
1. A + B = B + A (bersifat komutatif)
2. A + (B + C) = (A + B) + C (bersifat asosiatif)
3. A + O = O + A = A (O matriks identitas dari penjumlahan)
4. A + (-A) = (-A) + A = O (-A matriks invers penjumlahan)

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