matrices(form 5)
TRANSCRIPT
MATHEMATICS FORM 5
CHAPTER 4
SUMMARY
CONTENTS
REVISION
A matrix is a rectangular table of numbers.
The horizontal line in a matrix are called rows.
The vertical lines are called columns.
Number inside the matrix are called elements.
The order of matrix is in the form of m x n●m - number of rows ●n - number of columns
17
10
16
9
15
8
2 x 3
1st Row
2nd Row
1st Column2nd Column3rd Column
aaaaaa
232221
131211
2 x 3
Order
ih
gf
dc
ba
rqpdc
ba
Two matrices are equal, if only if, both have the same order and the same corresponding elements
Two matrices can be added or subtracted if they are of the same order. The process is by adding or subtracting the corresponding elements
idhc
gbfa
ih
gf
dc
ba
idhc
gbfa
ih
gf
dc
ba
LEARNING OUTCOMES
SUBTOPIC
LET’S DO IT
4.4B4.4A 4.4C 4.4D
4.4 Multiplication Of A Matrix By A Number
Learning Outcomes
Multiply A matrix by A number
Express A given matrix as A multiplication Of another matrix by A number
Perform calculation on matrices involvingAddition, subtraction and scalar multiplication
Solve matrix equations involving addition,Subtraction and scalar multiplication
a b c
d e fk
m x n
=a b c
d e f
k
kk
k
k
k
Multiplicand
Multiplier
m x n
Product
4.4A Multiplying Of A Matrix By A Number
Where k is a number
Multiplication of a matrix by a number is the process of multiplying each element in the matrix by that number.
Multiply:
1 8 -3
4 -2 53
2 x 3
=1 8 -3
4 -2 52 x 3
3X
3X
3X
3X
3X
3X
3 24 -9
12 -6 152 x 3
=
4.4B Expressing Of A Matrix
Expressing a Given Matrix as Multiplication of a Matrix by a
Number
a b c
d e f= pk
mk
rk
ok
qk
nk
p
m
r
o
q
n= k
Do It:
4 10
-16 -8= 2X
=
22
-8
5
-4
22X
2X(-8)
2X5
(-4)
Given that
84
13
26
A
12
34
05
Band
Find 3A+2B
= 36 2
3 1
-4 8
+ 2-5 0
4 3
2 -1
=6 2
3 1
-4 8
+3X 3X
3X
3X
3X
3X 2X
2X 2X
2X
2X
2X
-5 04 32 -1
4.4C Addition, Subtraction and Scalar Multiplication
= +18 6
9
-12
3
24
-10
8
4
0
6
-2
=18 (-10)+ +6 0
+9 8 +3 6
+-12 4 +24 -2
=8 6
17
-8
9
22
If 3a -2
1 6b3 -
4 -12
11
1=
2 6
-8 7
find the values of a and b
3a -2
1 6b3 -
4 -12
11
1=
2 6
-8 7
-4 -12
11
1=
2 6
-8 7
3X
3X 3X
3X-2
1 6b
3a
18b
- 4 -12
11
1=
2 6
-8 7
9a
3
-6
4 29a - =9a 2= 4+9a = 6
a = 23
18b
- 1 =718b
=7 1+18b
=8= b
49
dc
baA
dc
ba
dc
baAA
dc
ba
22
22
dc
ba2
Multiply:
2
2
187
a)
1
52
1
8b)
Multiply:
14
2
7562
2
187a)
8
40
4
1
52
1
8b)
Express each of the following matrices asthe multiplication of a matrix by a number.
816
104a)
1621
6270
3159b)
48
522
816
104a)
3
127
290
153
3
1621
6270
3159
b)
ARITHMATIC RULES
B-bracket
O-power of
D-division
M-multiplication
A-addition
S-subtraction
Given
02
34A , and
21
04B .
Find:
a) 2A+3B
b) 3A-2B
Given
02
34A , and
21
04B
a) 2A+3B
b) 3A-2B
61
64
48
920
Given
c
b
a
Y . Find Y if
0
1
8
7
2
3
3Y
Given
c
b
a
Y . Find Y if
0
1
8
7
2
3
3Y
3
71
3
11
Y
Worksheet 1 Worksheet 2
Multiply:
1 8 -3
4 -2 53
2 x 3
=1 8 -3
4 -2 52 x 3
3X
3X
3X
3X
3X
3X
3 24 -9
12 -6 152 x 3
=
= +18 6
9
-12
3
24
-10
8
4
0
6
-2
=18 (-10)+ +6 0
+9 8 +3 6
+-12 4 +24 -2
=8 6
17
-8
9
22
Do It:
4 10
-16 -8= 2X
=
22
-8
5
-4
22X
2X(-8)
2X5
(-4)
-4 -12
11
1=
2 6
-8 7
3X
3X 3X
3X-2
1 6b
3a
18b
- 4 -12
11
1=
2 6
-8 7
9a
3
-6
4 29a - =9a 2= 4+9a = 6
a = 23
18b
- 1 =718b
=7 1+18b
=8= b
49
a b cd e f = pk
mkrkok
qknk
Expressing Of A Matrix
pm
ro
qn= k
Multiplying Of A Matrix
a b cd e f
k
Addition, Subtraction and Scalar Multiplication
Problem Solving
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