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hitung invers matriks a jika invers tersebut ada

The determinant of matrix \( A \) is approximately \( -212 \). Since the determinant is not zero, the inverse of the matrix exists. I'll now calculate the inverse of matrix \( A \).The inverse of matrix \( A \) is:

\[
A^{-1} = \begin{pmatrix}
0.5283 & -0.4717 & 0.0755 & 0.0377 \\
-0.2547 & 0.2453 & -0.1792 & 0.1604 \\
-0.4481 & 0.3019 & 0.2217 & -0.0142 \\
0.2311 & -0.0189 & 0.0330 & -0.1085
\end{pmatrix}
\]

Let me know if you'd like a detailed breakdown of the calculation.

Would you like any further explanation or clarification?

Here are 5 related questions to expand on this topic:
1. How is the determinant of a matrix used to check for invertibility?
2. What are some methods to compute the inverse of a matrix manually?
3. Can any square matrix always have an inverse?
4. How do row operations relate to finding the inverse of a matrix?
5. What are some applications of matrix inverses in real-world problems?

**Tip**: When calculating the inverse manually, row-reduction (Gaussian elimination) is an effective method, but it can be tedious for large matrices.

Learn how to calculate the inverse of a matrix using determinants and adjoints. This problem explains how to find the inverse of a given 4x4 matrix with a step-by-step solution, suitable for advanced linear algebra students.

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