Converting graphs to matrices and understanding matrix equality.

2. Learning Intention and Success
Criteria
 Learning Intention: Students will understand the
relationship between graphs and matrices and the
features that define matrix equality
 Success Criteria: You will be able to convert a graph
to a matrix, and you will be able to use the concept of
matrix equality to solve simple equations.

3. From Graphs to Matrices
 The diagram on the left
represent the number of roads
between 4 towns
 This can be represented in a
matrix
𝐴 𝐵 𝐶 𝐷
𝐴
𝐵
𝐶
𝐷
1
 Example: element 1,3 represents
the number of roads from A to C
(which is 1)
Roads to town
Roads from
town

4. From Graphs to Matrices
 The diagram on the left
represent the number of roads
between 4 towns
 This can be represented in a
matrix
𝐴 𝐵 𝐶 𝐷
𝐴
𝐵
𝐶
𝐷
0 0
0 0
1 2
1 0
1 1
2 0
1 1
1 0
 Example: element 1,3 represents
the number of roads from A to C
(which is 1)
Roads to town
Roads from
town

5. Matrix Equality
 Two matrices are equal
only when:
 Their order is the same
 All of their elements are
the same
Example:
1 2
3 4
=
1 2
3 4
 We can use matrix
equality to calculate
unknown values within
matrices.
 Example on next page

6. Matrix Equality Example

1 𝑏
𝑐 𝑑
=
𝑎 3
4 𝑎 + 𝑏
.
Calculate the values of 𝑎, 𝑏, 𝑐 and 𝑑.
 Since the matrices are equal, each element is equal.
Therefore:
1 = 𝑎
𝑏 = 3
𝑐 = 4
𝑑 = 𝑎 + 𝑏
𝑑 = 1 + 3
𝑑 = 4