Matrix Calculator
Perform matrix addition, subtraction, and multiplication for 2x2 and 3x3 matrices.
Matrix Operations
Matrix A
Matrix B
Understanding Matrix Operations
Matrices are fundamental mathematical objects used in various fields like physics, engineering, computer graphics, and economics.
Matrix Addition/Subtraction:
Matrices must have the same dimensions. Operations are performed element-wise.
[c d] [g h] [c+g d+h]
Matrix Multiplication:
For A × B, the number of columns in A must equal the number of rows in B.
[c d] [g h] [ce+dg cf+dh]
Matrix Operation Examples
| Operation | Example | Result |
|---|---|---|
| Addition | [[1,2],[3,4]] + [[5,6],[7,8]] | [[6,8],[10,12]] |
| Subtraction | [[5,6],[7,8]] - [[1,2],[3,4]] | [[4,4],[4,4]] |
| Multiplication | [[1,2],[3,4]] * [[5,6],[7,8]] | [[19,22],[43,50]] |
Frequently Asked Questions
What is a matrix?
A matrix is a rectangular array of numbers, symbols, or expressions, arranged in rows and columns. Matrices are fundamental objects in linear algebra and are used to represent linear transformations, systems of linear equations, and data.
How do you add/subtract matrices?
To add or subtract matrices, they must have the same dimensions (same number of rows and columns). You simply add or subtract the corresponding elements in each matrix.
How do you multiply matrices?
To multiply two matrices, the number of columns in the first matrix must equal the number of rows in the second matrix. The result is a new matrix where each element is the dot product of a row from the first matrix and a column from the second matrix.