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.)
3.2
−3.6
2.3
−0.9
3.7
1.9
2.4
1.6
5.8
Solution
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:
Would you like more details or have any questions? Here are some related questions to expand your understanding:
- How can you check if a matrix is singular?
- What does it mean when a matrix has no inverse?
- What are the practical applications of matrix inversion?
- How does rounding affect matrix operations?
- 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.
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Math Problem Analysis
Mathematical Concepts
Linear Algebra
Matrix Inversion
Determinants
Singular Matrices
Formulas
Inverse of a 3x3 matrix formula: A⁻¹ = (1/det(A)) * adj(A)
Determinant formula for 3x3 matrix
Theorems
A matrix is invertible if and only if its determinant is non-zero
Suitable Grade Level
Undergraduate Level