Matrix Addition and Subtraction Calculator

Perform element-wise addition and subtraction of matrices with step-by-step solutions

Matrix Operations

Results

✓ Operation Successful
A + B = Result Matrix

Result Matrix (A + B)

[43]
[-27]

Matrix Properties

Dimensions: 2×2
Type: Square
Trace: 11
Zero Matrix: No

Step-by-Step Solution

1.Matrix Addition: C[i,j] = A[i,j] + B[i,j]
2.Adding corresponding elements from matrices A and B
3.C[1,1] = 3 + 1 = 4
4.C[1,2] = -1 + 4 = 3
5.C[2,1] = 0 + -2 = -2
6.C[2,2] = 2 + 5 = 7

Example Calculations

Matrix Addition Example

Matrix A:

[3 -1]
[0 2]

Matrix B:

[1 4]
[-2 5]

A + B:

[4 3]
[-2 7]

Matrix Subtraction Example

Matrix A:

[5 2]
[3 -1]

Matrix B:

[2 1]
[1 3]

A - B:

[3 1]
[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