Algebra

##### Related Lessons

- Adding and Subtracting Scientific Notation
- Adding Fractions
- Algebra Calculators
- Arithmetic Sequence
- Average Rate of Change
- Change of Base Formula
- Cm to M
- Commutative Property of Addition
- Completing the Square
- Cross Product Calculator
- Determinant Calculator
- Determinant of a Matrix
- Difference of Squares
- Discriminant
- Divisibility Rule for 7
- Dot Product Calculator
- Eigenvalue Calculator
- Eigenvector Calculator
- Equation of a Circle
- Even Numbers
- Exponent Rules
- Factorial Calculator
- Fractional Exponents
- How to Find the Median
- Interval Notation
- Matrix Addition
- Matrix Subtraction
- Midpoint Formula
- Multiplying Negative Numbers
- Negative Exponents
- Odd Numbers
- One to One Function
- Partial Fraction Decomposition Calculator
- Point Slope Form
- Properties of Multiplication
- Rationalize the Denominator
- Rectangular to Polar Calculator
- Reflexive Property
- Round to the Nearest Tenth
- RREF Calculator
- Slope Calculator
- Slope Intercept Form
- Standard Form
- Summation Calculator
- Vertex Form

Tutors/teachers:

Nikkolas

Tutor and Aerospace Engineer

# 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 = **

Result :

Worksheet 1

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Cheat sheet

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