Math Problem Statement

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

Solution

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!

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Math Problem Analysis

Mathematical Concepts

Linear Algebra
Matrix Inversion
Singular Matrix
Determinants

Formulas

Inverse of a matrix: A^-1 = 1/det(A) * adj(A)
Determinant of a 3x3 matrix

Theorems

A matrix is invertible if and only if its determinant is non-zero

Suitable Grade Level

Undergraduate (Linear Algebra Course)