Matrix Calculator

Advanced Linear Algebra Operations

A powerful tool for students of linear algebra, engineering, and computer science. This calculator performs basic matrix operations, including addition, subtraction, and multiplication.

The Formulas Explained

• Matrix Addition/Subtraction: Performed element-wise. The matrices must have the same dimensions. The element at [i, j] in the result is the sum or difference of the elements at [i, j] in the original matrices.
• Matrix Multiplication: To multiply matrix A (size m×n) by matrix B (size n×p), the number of columns in A must equal the number of rows in B. The resulting matrix will be of size m×p. Each element [i, j] in the result is the dot product of row i from A and column j from B.

How to Use the Calculator

1. Enter Matrices: Input the values for Matrix A and Matrix B in the text areas. Separate numbers in a row with commas, and separate rows with new lines.
2. Select Operation: Choose the operation (Add, Subtract, Multiply) from the dropdown menu.
3. Calculate: The resulting matrix will be displayed.

Real-World Example

Adding two 2x2 matrices:

• Matrix A: 1, 2 3, 4
• Matrix B: 5, 6 7, 8
• Result: 6, 8 10, 12

Multiplying the same matrices:

• Result[0,0] = (1*5 + 2*7) = 19
• Result[0,1] = (1*6 + 2*8) = 22
• Result[1,0] = (3*5 + 4*7) = 43
• Result[1,1] = (3*6 + 4*8) = 50
• Final Result: 19, 22 43, 50

Frequently Asked Questions (FAQ)

• What if my matrix dimensions don't match? The calculator will display an error. For addition and subtraction, matrices must be the same size. For multiplication (A × B), the number of columns in A must equal the number of rows in B.
• Can this calculator find the determinant or inverse? This version focuses on basic arithmetic. Calculating determinants and inverses are more complex operations not currently supported.
• How should I format the input? Use commas to separate numbers in a row and press Enter/Return to start a new row. Ensure all rows have the same number of columns.