Algebra

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# Matrix Subtraction

#### Lesson Contents

## How to Subtract Matrices

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

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

– =

### Rules of Matrix Subtraction

Matrix subtraction and matrix addition have the same rules. The operation for subtracting 2×3 matrices follows the same process as subtracting 2×2 matrices. The operation for subtracting 3×3 matrices follows the same process as well. The operation for subtracting 11×22 matrices also follows the same process.

In fact, **we can subtract matrices of any size as long as the two matrices being subtracted have the same dimension** (i.e. must both be 4×4 or must both be 2×9, etc). Make sure keep track of any negative numbers during matrix subtraction, they can get easily lost or sign flipped when working with a large matrix!

### Example Problem

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

Find the final matrix by subtracting the second matrix from the first matrix.

M1 = and M2 =

Solution:

The matrices are both 2×2, so they meet the requirement of having the same dimension. Let’s subtract the second matrix from the first by subtracting the numbers in like entry positions.

a1 – a2 = 6 – 5 = 1

b1 – b2 = 6 – 1 = 5

c1 – c2 = 10 – 2 = 8

d1 – d2 = 6 – 4 = 2

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