Algebra

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# Matrix Addition

#### Lesson Contents

## How to Add Matrices

**To add two matrices, we simply add the numbers that are in like entry positions. **Matrices must have the same dimension to be addable.

Here is what matrix addition for 2×2 matrices looks like:

+ =

### Rules of Matrix Addition

Matrix addition and matrix subtraction have the same rules. The operation for adding 2×3 matrices follows the same process as adding 2×2 matrices. The operation for adding 3×3 matrices follows the same process as well. The operation for adding 7×9 matrices also follows the same process.

In fact, **we can add matrices of any size as long as the two matrices being added have the same dimension** (i.e. must both be 5×5, or must both be 3×6, etc). Make sure keep track of any negative numbers during matrix addition, they can get easily lost when working with a large matrix!

### Example Problem

Here’s an example problem for 2×2 matrix addition.

Find the final matrix by adding the two matrices.

M1 = and M2 =

Solution:

The matrices are both 2×2, so they meet the requirement of having the same dimension. Let’s add the two matrices by adding the numbers in like entry positions.

a1 + a2 = 5 + 6 = 11

b1 + b2 = 8 + 2 = 10

c1 + c2 = 3 + 12 = 15

d1 + d2 = 6 + 2 = 8

Now let’s plug the numbers into our final matrix.**M1 + M2 =**