https://file.aiquickdraw.com/mathbot/file/17273621003292etg98ar.jpg

The image contains three matrix inversion problems. Let's go step by step to solve each part.

### Part a: Find the inverse of the matrix:
\[
A = \begin{bmatrix}
-2 & 3 & 2 \\
6 & 0 & 3 \\
4 & 1 & -1
\end{bmatrix}
\]
I'll calculate the inverse of this matrix first.The inverse of matrix \( A \) from part (a) is:

\[
A^{-1} = \begin{bmatrix}
-0.0417 & 0.0694 & 0.125 \\
0.25 & -0.0833 & 0.25 \\
0.0833 & 0.1944 & -0.25
\end{bmatrix}
\]

Now, let's solve part (b). The matrix is:
\[
B = \begin{bmatrix}
1 & 2 & -1 \\
0 & -1 & 2 \\
0 & 1 & 0
\end{bmatrix}
\]

I will compute the inverse of matrix \( B \) next.The inverse of matrix \( B \) from part (b) is:

\[
B^{-1} = \begin{bmatrix}
1 & 0.5 & -1.5 \\
0 & 0 & 1 \\
0 & 0.5 & 0.5
\end{bmatrix}
\]

Finally, let's solve part (c) for the matrix:
\[
C = \begin{bmatrix}
3 & 0 & 1 \\
0 & 2 & 1 \\
1 & 2 & 0
\end{bmatrix}
\]

I will now compute the inverse of matrix \( C \).It seems like I can’t do more advanced data analysis right now. Please try again later.

However, we have already solved parts (a) and (b). If you'd like, I can help guide you through the steps of solving part (c) manually or you can upload the image again.

Let me know how you'd like to proceed! Would you like any more details on the solved parts or to ask about any other specific topic?

Here are some related questions you might find helpful:
1. How can you verify the result of a matrix inverse?
2. What are the properties of an invertible matrix?
3. How can matrix inversion be applied in solving linear systems?
4. What does it mean if a matrix doesn't have an inverse?
5. Can you compute the determinant of a matrix to check invertibility?

**Tip:** A matrix is invertible only if its determinant is non-zero.

Find the inverse of the following matrices: a) [[-2, 3, 2], [6, 0, 3], [4, 1, -1]], b) [[1, 2, -1], [0, -1, 2], [0, 1, 0]], c) [[3, 0, 1], [0, 2, 1], [1, 2, 0]]

Step-by-step solutions to three matrix inversion problems involving 3x3 matrices. Learn how to calculate the inverse of matrices using linear algebra concepts, including the relation between the determinant and inverse.

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