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:
- What makes a matrix singular or non-invertible?
- How is the determinant of a matrix related to its invertibility?
- Can a matrix be nearly singular? What does that imply about its inverse?
- What methods can be used to find the inverse of a non-singular matrix manually?
- 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!
Ask a new question for Free
By Image
Drop file here or Click Here to upload
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)