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.

Matrix addition

1	-4	0
8	-1	6
0	3	2

9	3	7
-8	0	5
-3	2	9

Matrix addition

1	-4	0
8	-1	6
0	3	2

9	3	7
-8	0	5
-3	2	9

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	-4	0
8	-1	6
0	3	2

9	3	7
-8	0	5
-3	2	9

1 + 9	-4 + 3	0 + 7
8 + -8	-1 + 0	6 + 5
0 + -3	3 + 2	2 + 9

10	-1	7
0	-1	11
-3	5	11

Real-world 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	7	1
-2	0	4
8	-5	3

6	1	8
-3	0	9
-1	2	1

9 - 6	7 - 1	1 - 8
-2 - -3	0 - 0	4 - 9
8 - -1	-5 - 2	3 - 1

3	6	-7
1	0	-5
9	-7	2

1	-4	0
8	-1	6
0	3	2

9	3	7
-8	0	5
-3	2	9

1 + 9	-4 + 3	0 + 7
8 + -8	-1 + 0	6 + 5
0 + -3	3 + 2	2 + 9

10	-1	7
0	-1	11
-3	5	11

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	7	1
-2	0	4
8	-5	3

6	1	8
-3	0	9
-1	2	1

9 - 6	7 - 1	1 - 8
-2 - -3	0 - 0	4 - 9
8 - -1	-5 - 2	3 - 1

3	6	-7
1	0	-5
9	-7	2