Matriks tingkatan 5

2. 11 12 13 14
21 22 23 24
31 32 33 34
mn mn mn mn
a a a a
a a a a
a a a a
a a a a







 
Row 1
Row 2
Row 3
Row m
Column 1 Column 2 Column 3 Column 4

3. A matrix of m rows and n columns is called
a matrix with dimensions m x n.
2 3 4
1.) 1
1
2
π
 − 
 
 −
 
3 8 9
2.) 2 5
6 7 8
π
− 
 − 
 − 
10
3.)
7
 
 − 
[ ]4.) 3 4−
2 X 3
3 X 3
2 X 1
1 X 2

4. 3 5
1
1.) 4
4
0π
− 
 
 
 
 − 
3 0
2.)
0 3
− 
 
 
1 2 3
3.) 0 1 8
0 0 1
 
 
 
  
4.) 2π 
 
5
5.)
π
− 
 
 
[ ]6.) 3−
3 X 2 2 X 2 3 X 3
1 X 2 2 X 1 1 X 1

6. To add matrices, we add the corresponding
elements. They must have the same
dimensions.
5 0 6 3
4 1 2 3
A B
− −   
= =   
   
A + B
5 6 0 3
4 2 1 3
− + + − 
=  + + 
1 3
6 4
− 
=  
 

7. 2 1 3 0 0 0
2.)
1 0 1 0 0 0
−   
+   −   
2 1 3
1 0 1
− 
=  − 
When a zero matrix is added to another
matrix of the same dimension, that same
matrix is obtained.

8. To subtract matrices, we subtract the
corresponding elements. The matrices must
have the same dimensions.
1 2 1 1
3.) 2 0 1 3
3 1 2 3
−   
   − −   
   − −   
1 1 2 ( 1)
2 1 0 3
3 2 1 3
− − − 
 − − − 
 − − − − 
0 3
3 3
5 4
 
 = − − 
 − − 

9. 4 1 6 5
1.)
6 3 7 3
− − −   
+   −   
1 3 2 2 1 5
2.)
4 0 5 6 4 3
− −   
−   −   
2 6
13 0
− − 
=  
 
1 4 7
2 4 8
− − 
=  − − 

10. ADDITIVE INVERSE OF A MATRIX:
1 0 2
3 1 5
A
 
=  − 
1 0 2
3 1 5
A
− − 
− =  − − 

11. Find the additive inverse:
2 1 5
6 4 3
− 
 − 
2 1 5
6 4 3
− − 
=  − − 

12. Scalar Multiplication:
1 2 3
1 2 3
4 5 6
k
 
 − − − 
 − 
We multiply each # inside our matrix by
k.
1 2 3
1 2 3
4 5 6
k k k
k k k
k k k
 
 = − − − 
 − 

13. 3 0
1.) 3
4 5
− 
 
 
9 0
12 15
− 
=  
 
2
1 2
2.) 5 4 1
0 5
x
y
x
− 
 
 
 − 
2
5 10 5
20 5 5
0 25 5
x
y
x
− 
 =  
 − 

15. 





=













−−
+




 −
812
026
2
14
58
13
2
y
x






=





−−
+−+
812
026
528
1143
2
y
x

16. 





=





−
+
812
026
56
043
2
y
x






=





−
+
812
026
21012
086
y
x
Scalar Multiplication:

17. 6x+8=26
6x=18
x=3
10-2y=8
-2y=-2
y=1

18. • Associative Property of Addition
(A+B)+C = A+(B+C)
• Commutative Property of Addition
A+B = B+A
• Distributive Property of Addition and
Subtraction S(A+B) = SA+SB
S(A-B) = SA-SB
• NOTE: Multiplication is not included!!!