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. First, study the figure below carefully to see how it is done for a 2x2 matrix.

Add and subtract matrices

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.

More examples showing how to add and subtract matrices

Matrix addition


Add the two matrices shown below:

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

Matrix addition


Add the two matrices shown below:

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
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

Matrix subtraction

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

Subtract the two matrices below:

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

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

Subtract the two matrices below:

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

Real-world connection

You have a business selling shirts and pants. The matrices below represent the number of shirts and pants that you sold in two weeks. The matrix on the left is week #1 and the matrix on the right is week #2.

Row #1 represents number of pants that you sold and row #2 represents number of shirts that you 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?

Just perform matrix addition!

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

Real-world connection

You have a business selling shirts and pants. The matrices below represent the number of shirts and pants that you sold in two weeks. The matrix on the left is week #1 and the matrix on the right is week #2.

Row #1 represents number of pants that you sold and row #2 represents number of shirts that you 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?

Just perform matrix addition!

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

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

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