Matrix Rank Calculator

How to Use the Matrix Rank Calculator

1. Enter the number of rows and columns for your matrix using the input fields.
2. Click "Generate Matrix" (if available) or manually enter the matrix elements in the grid.
3. Click the "Calculate" button to determine the rank of the matrix.
4. The result will be displayed as the maximum number of linearly independent rows or columns.

Understanding Matrix Rank

The rank of a matrix is a fundamental concept in linear algebra that represents the maximum number of linearly independent row or column vectors in the matrix. It provides important information about the matrix's properties and is used in various applications including:

• Solving systems of linear equations
• Matrix inversion
• Data analysis and dimensionality reduction
• Rank deficiency identification

How the Calculator Works

This calculator uses Gaussian elimination to determine the matrix rank. The process involves:

1. Creating an augmented matrix from the original matrix
2. Performing row operations to transform the matrix into row echelon form
3. Counting the number of non-zero rows in the resulting matrix, which represents the rank

Example

Consider the following 3×3 matrix:

A = [[1, 2, 3], [2, 4, 6], [1, 1, 1]]

When you input this matrix into the calculator, the rank will be 2 because the second and third rows are linearly dependent on the first row.