Matrix Calculator

What is a Matrix?

[Image of matrix math concept]

A Matrix (plural: Matrices) is a rectangular array of numbers arranged in rows and columns. It is a fundamental concept in linear algebra used to solve systems of linear equations, transform geometric shapes (in 3D graphics), and handle large datasets in computer science.

A matrix with m rows and n columns is called an m × n matrix.

Matrix Operations Explained

1. Addition & Subtraction (A ± B)

To add or subtract two matrices, they must have the same dimensions (same number of rows and columns). You simply add or subtract the corresponding elements.

2. Multiplication (A × B)

This is the tricky part. You can multiply Matrix A and Matrix B *only if* the number of columns in A equals the number of rows in B.
The result will have dimensions: (Rows of A) × (Cols of B).
We calculate the "Dot Product" of rows from A and columns from B.

3. Determinant |A|

The determinant is a special number calculated from a square matrix (2x2, 3x3, etc.). It helps determine if a matrix has an inverse. If Det = 0, the matrix is "singular" and has no inverse.

• 2x2 Determinant: ad - bc

4. Transpose (Aᵀ)

To find the transpose, you simply swap the rows and columns. The first row becomes the first column, and so on.