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.)
[3.59 1.22
−1.02 0]
Solution
The inverse of the given matrix, rounded to two decimal places, is:
-0.00 & -0.98 \\ 0.82 & 2.88 \end{pmatrix}$$ Let me know if you'd like further details or have any questions! Here are 5 related questions for practice: 1. What conditions must be met for a matrix to have an inverse? 2. How do you calculate the determinant of a 2x2 matrix? 3. What does it mean if a matrix has no inverse (i.e., is singular)? 4. How can you verify if the calculated inverse is correct? 5. How does the inverse of a matrix relate to solving systems of linear equations? **Tip:** For a 2x2 matrix, the inverse exists if and only if the determinant is non-zero. Always check the determinant first!Ask a new question for Free
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Math Problem Analysis
Mathematical Concepts
Linear Algebra
Matrix Inversion
Determinants
Formulas
Inverse of a 2x2 matrix: A⁻¹ = (1/det(A)) * adj(A), where det(A) = ad - bc
Theorems
Inverse Matrix Theorem
Determinant Formula
Suitable Grade Level
Grades 10-12