https://file.aiquickdraw.com/mathbot/file/1727177746341jfaop0io.jpg

The matrix provided in the image is:

\[
A = \begin{pmatrix}
0 & 10 & 0 & 2 \\
0 & 5 & 0 & 1 \\
-3 & 4 & -1 & 0 \\
-8 & 7 & 1 & 6
\end{pmatrix}
\]

To find the inverse of matrix \( A \) (denoted as \( A^{-1} \)), we typically use methods such as:

1. **Gaussian Elimination**: Augment the matrix \( A \) with the identity matrix and perform row operations until the left side becomes the identity matrix. The right side will then be \( A^{-1} \).
  
2. **Adjoint Method**: Calculate the adjoint of the matrix and then divide by the determinant.

3. **LU Decomposition**: Decompose the matrix into lower and upper triangular matrices, then find the inverse using forward and backward substitution.

Given that this is a \( 4 \times 4 \) matrix, finding the inverse manually can be cumbersome. Would you like a step-by-step explanation of how to find \( A^{-1} \) using a specific method, or shall I calculate the inverse for you directly?

Learn how to find the inverse of a 4x4 matrix using methods like Gaussian elimination and the adjoint formula. This problem covers key concepts in matrix algebra and is suitable for undergraduate students.

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