Matrix Addition and Subtraction Calculator
Perform element-wise addition and subtraction of matrices with step-by-step solutions
Matrix Operations
Results
Result Matrix (A + B)
Matrix Properties
Step-by-Step Solution
Example Calculations
Matrix Addition Example
Matrix A:
[0 2]
Matrix B:
[-2 5]
A + B:
[-2 7]
Matrix Subtraction Example
Matrix A:
[3 -1]
Matrix B:
[1 3]
A - B:
[2 -4]
Matrix Operation Rules
Same Dimensions
Both matrices must have identical dimensions
Same number of rows and columns
Element-wise Operation
Add/subtract corresponding elements
C[i,j] = A[i,j] ± B[i,j]
Commutative (Addition)
A + B = B + A
Order doesn't matter for addition
Matrix Properties
Associative: (A + B) + C = A + (B + C)
Identity: A + 0 = A (zero matrix)
Inverse: A + (-A) = 0
Distributive: k(A + B) = kA + kB
Non-commutative (Sub): A - B ≠ B - A
Understanding Matrix Addition and Subtraction
What is Matrix Addition?
Matrix addition is the operation of adding two matrices by adding the corresponding entries together. This operation is only defined for matrices that have the same dimensions (same number of rows and columns).
Requirements
- •Same dimensions: Both matrices must be m×n
- •Element-wise operation: Add corresponding positions
- •Result dimensions: Same as input matrices
Mathematical Formula
For matrices A and B:
Addition: C[i,j] = A[i,j] + B[i,j]
Subtraction: C[i,j] = A[i,j] - B[i,j]
Real-world Applications
- •Budget tracking and financial planning
- •Image processing and computer graphics
- •Engineering simulations and data analysis