Use technology to find the inverse of the given matrix (when it exists). Round all entries in your answer to two decimal places. (Caution: Because of rounding errors, technology sometimes produces an "inverse" of a singular matrix. These often can be recognized by their huge entries. If the inverse doesn't exist, enter DNE in any cell of the matrix.)

3.2

−3.6

2.3

−0.9

3.7

1.9

2.4

1.6

5.8

The matrix provided is singular, as indicated by the extremely large entries in the "inverse," which is a common result of rounding errors when a singular matrix is mistakenly processed as invertible. Therefore, the inverse of this matrix does not exist.

The correct answer is:

\[
\text{DNE}
\]

Would you like more details or have any questions? Here are some related questions to expand your understanding:

1. How can you check if a matrix is singular?
2. What does it mean when a matrix has no inverse?
3. What are the practical applications of matrix inversion?
4. How does rounding affect matrix operations?
5. How can singular matrices appear in real-world problems?

**Tip**: If a matrix is singular, its determinant will be zero, which is a quick way to check invertibility.

Use technology to find the inverse of the given matrix (when it exists). Round all entries in your answer to two decimal places. (Caution: Because of rounding errors, technology sometimes produces an "inverse" of a singular matrix. These often can be recognized by their huge entries. If the inverse doesn't exist, enter DNE in any cell of the matrix.)

3.2, -3.6, 2.3
-0.9, 3.7, 1.9
2.4, 1.6, 5.8

Use technology to determine if the inverse of a 3x3 matrix exists, with caution on rounding errors. This example demonstrates the concept of singular matrices and how to check if a matrix has no inverse by calculating the determinant.

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