Add and Subtract Matrices
It is easy to add and subtract matrices. If you know how to add and subtract integers, this lesson will be a piece of cake
The important rule to know is that when adding and subtracting matrices, first make sure the matrices have the same dimensions.
In order words, you can add or subtract a 2x3 with a 2x3 or a 3x3 with a 3x3. However, you cannot add a 3x2 with a 2x3 or a 2x2 with a 3x3.
Rule to follow in order to add and subtract matrices.
You can add elements in the same position or elements in the same row and same column. We show these elements with the same color to make this crystal clear
1 + 9

4 + 3

0 + 7

8 + 8

1 + 0

6 + 5

0 + 3

3 + 2

2 + 9

Realworld connection
You have a business selling shirts and pants. The matrices below represent the number of shirts and pants sold in two weeks
Row #1 represents number of pants sold and row #2 represents number of shirts sold from Monday to Friday
For example, you sold 40 pants on Wednesday (week 1).
You sold 28 shirts on Friday (week 2)
How many pants and shirts have you sold in two weeks?
Week 1

Week 2

50

25

40

80

10

30

90

60

12

45


20

30

70

65

80

55

35

75

14

28


50 + 20

25 + 30

40 + 70

80 + 65

10 + 80

30 + 55

90 + 35

60 + 75

12 + 14

45 + 28

70

55

110

145

90

85

125

135

26

73

Matrix subtraction
Matrix subtraction is similar to matrix addition with the exception that you are subtracting elements in the same row and same column
9  6

7  1

1  8

2  3

0  0

4  9

8  1

5  2

3  1

Rule to follow in order to add and subtract matrices.
You can add elements in the same position or elements in the same row and same column. We show these elements with the same color to make this crystal clear
1 + 9

4 + 3

0 + 7

8 + 8

1 + 0

6 + 5

0 + 3

3 + 2

2 + 9

Realworld connection
You have a business selling shirts and pants. The matrices below represent the number of shirts and pants sold in two weeks
Row #1 represents number of pants sold and row #2 represents number of shirts sold from Monday to Friday
For example, you sold 40 pants on Wednesday (week 1).
You sold 28 shirts on Friday (week 2)
How many pants and shirts have you sold in two weeks?
Week 1

Week 2

50

25

40

80

10

30

90

60

12

45


20

30

70

65

80

55

35

75

14

28


50 + 20

25 + 30

40 + 70

80 + 65

10 + 80

30 + 55

90 + 35

60 + 75

12 + 14

45 + 28

70

55

110

145

90

85

125

135

26

73

Matrix subtraction
Matrix subtraction is similar to matrix addition with the exception that you are subtracting elements in the same row and same column
9  6

7  1

1  8

2  3

0  0

4  9

8  1

5  2

3  1

Add and subtract matrices quiz. Check how well you understand this lesson.
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