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.)

−1.3	0.8	−3.3

−0.8	−1.4	2.7
−2.2	−0.8	−0.2

The given matrix does not have an inverse, as it is singular. Therefore, the inverse does not exist (DNE).

Do you have any further questions or want more details?

Here are five related questions:
1. What makes a matrix singular or non-invertible?
2. How is the determinant of a matrix related to its invertibility?
3. Can a matrix be nearly singular? What does that imply about its inverse?
4. What methods can be used to find the inverse of a non-singular matrix manually?
5. How do rounding errors affect calculations with inverse matrices?

**Tip:** When dealing with matrices, always check the determinant first to ensure it's non-zero before attempting to find the inverse!

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.)

Matrix:
−1.3  0.8  −3.3
−0.8  −1.4  2.7
−2.2  −0.8  −0.2

Explore how to determine if a 3x3 matrix is invertible using technology. Learn about singular matrices, matrix inversion, and the role of the determinant in deciding invertibility. This problem involves calculating the determinant of the matrix and understanding when an inverse does not exist.

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