Matrices Rank Calculator

The Matrices Rank Calculator helps determine the rank of a given matrix. The rank of a matrix represents the maximum number of linearly independent rows or columns in the matrix. This tool uses a simplified Gaussian elimination approach to compute the rank.

How the Rank is Calculated

The matrix rank is calculated using row reduction (Gaussian elimination). The process involves transforming the matrix into its row echelon form, then counting the non-zero rows.

Input Format

• Enter the matrix with rows separated by commas.
• Each row's elements should be separated by spaces.
• Example: For the matrix
  \[
  \begin{bmatrix}
  1 & 2 & 3 \
  4 & 5 & 6 \
  7 & 8 & 9
  \end{bmatrix}
  \]
  Input should be: 1 2 3, 4 5 6, 7 8 9

Example Calculation

For the matrix
\[
\begin{bmatrix}
1 & 2 & 3 \
4 & 5 & 6 \
7 & 8 & 9
\end{bmatrix}
\]
The rank is 2 because only two rows are linearly independent.

Importance and Usage Scenarios

Matrix rank is crucial in linear algebra, systems of equations, and machine learning for determining solution spaces and dependency in variables.