Matrix Inverse Calculator

This calculator is designed for students and professionals who need to compute the inverse of a matrix. It simplifies the complex arithmetic involved in linear algebra.

Calculator

Results

Inverse Matrix:

            

Authoritative Content

Data Source and Methodology

All calculations are based on standard linear algebraic methods as outlined in "Introduction to Linear Algebra" by Gilbert Strang. All results adhere strictly to these methodologies.

The Formula Explained

The inverse of a matrix \( A \) is calculated using the formula:

\( A^{-1} = \frac{1}{\text{det}(A)} \text{adj}(A) \)

Glossary of Terms

How It Works: A Step-by-Step Example

To find the inverse of a 2x2 matrix \(\begin{pmatrix} a & b \\ c & d \end{pmatrix}\), use:

\( A^{-1} = \frac{1}{ad-bc} \begin{pmatrix} d & -b \\ -c & a \end{pmatrix} \)

Frequently Asked Questions (FAQ)

1. What is a matrix inverse?
An inverse matrix is a matrix that, when multiplied by the original matrix, results in an identity matrix.

2. Can all matrices be inverted?
No, only square matrices with a non-zero determinant can be inverted.

3. What is the use of matrix inversion?
Matrix inversion is used in solving linear equations, computer graphics, and more.

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