Matrix Subtraction Calculator (2×2 Matrices)
Enter Values for Two Matrices
What Is Matrix Subtraction?
Matrix subtraction is similar to matrix addition but instead involves subtracting corresponding elements.
If A = [aij] and B = [bij], the difference C = A - B is C = [cij] where
cij = aij - bij.
Rules for Matrix Subtraction
- Both matrices must have the same number of rows and columns.
- Subtract each element of B from the corresponding element of A.
- The result is a new matrix with the same dimensions.
Example 1: 2×2 Matrices
Matrix A:
| 7 5 |
| 4 6 |
Matrix B:
| 3 2 |
| 1 4 |
Difference C = A - B:
| 7-3 5-2 |
| 4-1 6-4 | = | 4 3 |
| 3 2 |
Properties of Matrix Subtraction
- Non-commutative: A - B ≠ B - A
- Subtracting zero: A - 0 = A
- Can be combined with addition: (A + B) - B = A
Applications of Matrix Subtraction
- Finding changes in datasets over time
- Calculating differences in transformations
- Physics: computing net forces or velocities represented as matrices
Common Mistakes
- Attempting to subtract matrices of different sizes
- Mixing up which matrix is being subtracted from which
- Forgetting negative signs in the subtraction
Frequently Asked Questions
Can I subtract matrices of different dimensions?
No. Both matrices must have the same number of rows and columns.
Is matrix subtraction commutative?
No. A - B is generally not equal to B - A.
Conclusion
Matrix subtraction is a fundamental operation in linear algebra. It is essential for calculating differences between datasets, transformations, and physical quantities represented in matrix form. This calculator allows you to perform matrix subtraction easily while reinforcing your understanding of the concept.