Matrix Rank Calculator
This tool helps you calculate the rank of a matrix, which is a fundamental concept in linear algebra. It is designed for students and professionals who need a quick and reliable solution.
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Matrix Rank:
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Data Source and Methodology
All calculations are strictly based on standard linear algebra techniques and verified algorithms.
The Formula Explained
\( \text{Rank}(A) = \text{number of non-zero rows in } A \text{ after row reduction} \)
Glossary of Terms
- Matrix: A rectangular array of numbers arranged in rows and columns.
- Rank: The dimension of the vector space spanned by the rows or columns of the matrix.
How It Works: A Step-by-Step Example
For matrix \( A = \begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix} \), the rank is calculated by reducing it to row echelon form.
Frequently Asked Questions (FAQ)
What is the rank of a matrix?
The rank of a matrix is the dimension of the vector space generated by its rows or columns.
Why is matrix rank important?
It is crucial in determining the solutions of linear systems and the invertibility of matrices.