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Adding and Subtracting Matrices

Adding and subtracting values in a matrix is incredibly simple! In fact, all you have to do is match up the position in the matrix with another matrix, and add the values together to create your matrix with the answers. For this reason, you can only add and subtract matrices of the same shape; 3x3, 4x4, etc. You cannot add or subtract a 3x3 matrix with a 3x4 matrix!

Let's have an example:

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

 

To add these matrices, simply get the value of each element from both matrices, and add them together:

(2+4) = 6 (5+6) = 11 (1+ -2) = -1
(4 + -1) = 3 (-3 + 5) = 2 (7+3) = 10
(5+9) = 14 (8+0) = 8 (6+4) = 10


Matrix 1 + Matrix 2:
6 11 -1
3 2 10
14 8 10

 

And for subtraction, you do the same thing except you subtract instead of add:

(2-4) = -2 (5-6) = -1 (1- -2) = 3
(4 - -1) = 5 (-3 - 5) = -8 (7-3) = 4
(5-9) = -4 (8-0) = 8 (6-4) = 2


Matrix 1 - Matrix 2:
-2 -1 3
5 -5 4
-4 8 2

It really is that easy!

You only have two things to remember:

1. You can only add or subtract matrices of the same size.
2. Make sure you are adding the same element from both matrices!

 

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