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IB Revision Lesson 4
28 5
26 22 =
“scalar”
2 x 28 2 x 5
2 x 26 2 x 2
56 10
52 4=
Easy... multiply each element
of the matrix by the scalar
“element” one matrix
two matrices
IB Revision Lesson 4
Cereal
Bread
Potatoe
s
Paula 2 4 5
Greg 1 7 3
Pã
o de
Açuca
r
Qu
itan
da
Cereal 120 110
Bread 55 60
Potatoes 35 30
Paula and Greg want to compare the cost of shopping at two supermarkets.
Pão de
Açucar
Qu
itan
da
Paula
Greg
IB Revision Lesson 4
Cereal
Bread
Potatoe
s
Paula 2 4 5
Greg 1 7 3
Pã
o de
Açuca
r
Qu
itan
da
Cereal 120 110
Bread 55 60
Potatoes 35 30
Paula and Greg want to compare the cost of shopping at two supermarkets.
Pão de
Açucar
Qu
itan
da
Paula
Greg
(2 x 3) x (3 x 2) (2 x 2)
The number of columns in the first must equal the number of rows in the
second
IB Revision Lesson 4
Cereal
Bread
Potatoe
s
Paula 2 4 5
Greg 1 7 3
Pã
o de
Açuca
r
Qu
itan
da
Cereal 120 110
Bread 55 60
Potatoes 35 30
The element in the product tells us the row of the first and the column of the second
Pão de
Açucar
Qu
itan
da
Paula
Greg
(2 x 120)
IB Revision Lesson 4
Cereal
Bread
Potatoe
s
Paula 2 4 5
Greg 1 7 3
Pã
o de
Açuca
r
Qu
itan
da
Cereal 120 110
Bread 55 60
Potatoes 35 30 Pão de
Açucar
Qu
itan
da
Paula
Greg
(2 x 120) + (4 x 55)
The element in the product tells us the row of the first and the column of the second
IB Revision Lesson 4
Cereal
Bread
Potatoe
s
Paula 2 4 5
Greg 1 7 3
Pã
o de
Açuca
r
Qu
itan
da
Cereal 120 110
Bread 55 60
Potatoes 35 30 Pão de
Açucar
Qu
itan
da
Paula
Greg
(2 x 120) + (4 x 55) + (5 x 35) = 635
The element in the product tells us the row of the first and the column of the second
IB Revision Lesson 4
Cereal
Bread
Potatoe
s
Paula 2 4 5
Greg 1 7 3
Pã
o de
Açuca
r
Qu
itan
da
Cereal 120 110
Bread 55 60
Potatoes 35 30 Pão de
Açucar
Qu
itan
da
Paula
Greg
(2 x 120) + (4 x 55) + (5 x 35) = 635
The element in the product tells us the row of the first and the column of the second
IB Revision Lesson 4
Cereal
Bread
Potatoe
s
Paula 2 4 5
Greg 1 7 3
Pã
o de
Açuca
r
Qu
itan
da
Cereal 120 110
Bread 55 60
Potatoes 35 30 Pão de
Açucar
Qu
itan
da
Paula
Greg
(2 x 120) + (4 x 55) + (5 x 35) = 635
(2 x 110)
The element in the product tells us the row of the first and the column of the second
IB Revision Lesson 4
Cereal
Bread
Potatoe
s
Paula 2 4 5
Greg 1 7 3
Pã
o de
Açuca
r
Qu
itan
da
Cereal 120 110
Bread 55 60
Potatoes 35 30 Pão de
Açucar
Qu
itan
da
Paula
Greg
(2 x 120) + (4 x 55) + (5 x 35) = 635
(2 x 110) + (4 x 60)
The element in the product tells us the row of the first and the column of the second
IB Revision Lesson 4
Cereal
Bread
Potatoe
s
Paula 2 4 5
Greg 1 7 3
Pã
o de
Açuca
r
Qu
itan
da
Cereal 120 110
Bread 55 60
Potatoes 35 30 Pão de
Açucar
Qu
itan
da
Paula
Greg
(2 x 120) + (4 x 55) + (5 x 35) = 635
(2 x 110) + (4 x 60) + (5 x 30) = 610
The element in the product tells us the row of the first and the column of the second
IB Revision Lesson 4
Cereal
Bread
Potatoe
s
Paula 2 4 5
Greg 1 7 3
Pã
o de
Açuca
r
Qu
itan
da
Cereal 120 110
Bread 55 60
Potatoes 35 30 Pão de
Açucar
Qu
itan
da
Paula
Greg
(2 x 120) + (4 x 55) + (5 x 35) = 635
(2 x 110) + (4 x 60) + (5 x 30) = 610
(1 x 120) +
The element in the product tells us the row of the first and the column of the second
IB Revision Lesson 4
Cereal
Bread
Potatoe
s
Paula 2 4 5
Greg 1 7 3
Pã
o de
Açuca
r
Qu
itan
da
Cereal 120 110
Bread 55 60
Potatoes 35 30 Pão de
Açucar
Qu
itan
da
Paula
Greg
(2 x 120) + (4 x 55) + (5 x 35) = 635
(2 x 110) + (4 x 60) + (5 x 30) = 610
(1 x 120) + (7 x 55) +
The element in the product tells us the row of the first and the column of the second
IB Revision Lesson 4
Cereal
Bread
Potatoe
s
Paula 2 4 5
Greg 1 7 3
Pã
o de
Açuca
r
Qu
itan
da
Cereal 120 110
Bread 55 60
Potatoes 35 30 Pão de
Açucar
Qu
itan
da
Paula
Greg
(2 x 120) + (4 x 55) + (5 x 35) = 635
(2 x 110) + (4 x 60) + (5 x 30) = 610
(1 x 120) + (7 x 55) + (3 x 35) = 610
The element in the product tells us the row of the first and the column of the second
IB Revision Lesson 4
Cereal
Bread
Potatoe
s
Paula 2 4 5
Greg 1 7 3
Pã
o de
Açuca
r
Qu
itan
da
Cereal 120 110
Bread 55 60
Potatoes 35 30 Pão de
Açucar
Qu
itan
da
Paula
Greg
(2 x 120) + (4 x 55) + (5 x 35) = 635
(2 x 110) + (4 x 60) + (5 x 30) = 610
(1 x 120) + (7 x 55) + (3 x 35) = 610
(1 x 110)
The element in the product tells us the row of the first and the column of the second
IB Revision Lesson 4
Cereal
Bread
Potatoe
s
Paula 2 4 5
Greg 1 7 3
Pã
o de
Açuca
r
Qu
itan
da
Cereal 120 110
Bread 55 60
Potatoes 35 30 Pão de
Açucar
Qu
itan
da
Paula
Greg
(2 x 120) + (4 x 55) + (5 x 35) = 635
(2 x 110) + (4 x 60) + (5 x 30) = 610
(1 x 120) + (7 x 55) + (3 x 35) = 610
(1 x 110) + (7 x 60) +
The element in the product tells us the row of the first and the column of the second
IB Revision Lesson 4
Cereal
Bread
Potatoe
s
Paula 2 4 5
Greg 1 7 3
Pã
o de
Açuca
r
Qu
itan
da
Cereal 120 110
Bread 55 60
Potatoes 35 30 Pão de
Açucar
Qu
itan
da
Paula
Greg
(2 x 120) + (4 x 55) + (5 x 35) = 635
(2 x 110) + (4 x 60) + (5 x 30) = 610
(1 x 120) + (7 x 55) + (3 x 35) = 610
(1 x 110) + (7 x 60) + (3 x 30) = 620
The element in the product tells us the row of the first and the column of the second
IB Revision Lesson 4
Cereal
Bread
Potatoe
s
Paula 2 4 5
Greg 1 7 3
Pã
o de
Açuca
r
Qu
itan
da
Cereal 120 110
Bread 55 60
Potatoes 35 30 Pão de
Açucar
Qu
itan
da
Paula
Greg
(2 x 120) + (4 x 55) + (5 x 35) = 635
(2 x 110) + (4 x 60) + (5 x 30) = 610
(1 x 120) + (7 x 55) + (3 x 35) = 610
(1 x 110) + (7 x 60) + (3 x 30) = 620
The element in the product tells us the row of the first and the column of the second
IB Revision Lesson 4
4 -1 2
3 6 -4
3 1 0
-2 4 6
7 2 -1=
The element in the product tells us the row of the first and the column of the second
IB Revision Lesson 4
4 -1 2
3 6 -4
3 1 0
-2 4 6
7 2 -1=
The element in the product tells us the row of the first and the column of the second
IB Revision Lesson 4
4 -1 2
3 6 -4
3 1 0
-2 4 6
7 2 -1=
The element in the product tells us the row of the first and the column of the second
IB Revision Lesson 4
4 -1 2
3 6 -4
3 1 0
-2 4 6
7 2 -1=
The element in the product tells us the row of the first and the column of the second
IB Revision Lesson 4
4 -1 2
3 6 -4
3 1 0
-2 4 6
7 2 -1=
The element in the product tells us the row of the first and the column of the second
IB Revision Lesson 4
4 -1 2
3 6 -4
3 1 0
-2 4 6
7 2 -1=
The element in the product tells us the row of the first and the column of the second
IB Revision Lesson 4
A-1 is the inverse of A
A x A-1 = I
ad – bc = determinant
(i.e. tells us about the inverse)
Det(A) = 0: A-1 does not existDet(A) = 1: A is “singular”
Det(A) ≠ 1: A is “non-singular”
IB Revision Lesson 4
IB Revision Lesson 4
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