https://file.aiquickdraw.com/mathbot/file/17267663895243nnkpw8z.jpg

The inverse of the matrix \( A \) using the Gauss-Jordan method is:

\[
A^{-1} = \begin{pmatrix}
-0.25 & 0.75 & 0.5 \\
0.125 & -0.375 & 0.25 \\
0.125 & 0.625 & 0.25
\end{pmatrix}
\]

Let me know if you need further details on how this inverse was obtained or if you would like to see the full steps of the Gauss-Jordan elimination.

Here are some related questions:

1. How does the Gauss-Jordan method differ from Gaussian elimination in finding matrix inverses?
2. Can every square matrix be inverted using Gauss-Jordan elimination?
3. How can you verify that a matrix and its inverse are correct?
4. What are the practical applications of finding a matrix inverse?
5. How does the inverse matrix relate to solving systems of linear equations?

**Tip:** Always verify the result of an inverse by multiplying the original matrix by its inverse; the product should be the identity matrix.

Find the inverse of the matrix A using Gauss-Jordan Method where A = [[-2, 1, 3], [0, -1, 1], [1, 2, 0]]

Learn how to find the inverse of a 3x3 matrix A using the Gauss-Jordan elimination method. This detailed solution includes step-by-step instructions on applying the row-reduction technique to matrix A = [[-2, 1, 3], [0, -1, 1], [1, 2, 0]]. Suitable for students in Grades 10-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation